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School: Berkeley
Course: STATISTICS
Stat 20 Quiz 1 February 10, 2014 Please write your name below and circle your section. Answer the questions in the space provided. There are questions on the back. This quiz covers material from Homeworks 1 a
School: Berkeley
Course: Theoretical Statistics
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 5 - Solutions Fall 2008 Issued: Tuesday, September 29, 2009 Problem 5.1 First, notice that we can rewrite: p(x; ) = exp [x log log ( log(1 )] so p belongs
School: Berkeley
Course: STAT 21
Quiz 1 Statistics 21 Spring 2010 Ibser 1. A large class takes a test, and the table shows their scores. For all parts of this problem, assume that the scores are continuous and that they are evenly distributed within each separate class interval. The maxi
School: Berkeley
Course: Probability
Retention Factor (Rf)! Not a Physical Constant! Rf = ! distance to ! midpoint! of spot! distance to ! solvent front! Rf depends on:! u The stationary phase ! u The mobile phase ! u The amount of compound! spotted! u The temperature! TLC: Conclusions! Give
School: Berkeley
STAT516 Solution to Homework 2 1.4.5: a) Let U1=(urn 1 chosen), U2=(urn 2 chosen), B=(black ball chosen), W=(White ball chosen). 2/5 B 1/2 U1 3/5 4/7 W B 1/2 U2 3/7 W b) P(U1)=1/2=P(U2); P(W|U1)=3/5; P(B|U1)=2/5; P(W|U2)=3/7; P(B|U2)=4/7 c) P(B)=P(B|U1)P(
School: Berkeley
UC Berkeley Department of Electrical Engineering and Computer Science Department of Statistics EECS 281A / STAT 241A Statistical Learning Theory Solutions to Problem Set 3 Fall 2011 Issued: Monday, October 10, 2011 Due: Monday, October 24, 2011 Reading: F
School: Berkeley
Course: STATISTICS
Chapter 23: accuracy of averages Context: previous chapters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Context: previous chapters . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
School: Berkeley
Course: STATISTICS
Chapter 26: tests of significance Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Tax revenue example Example . . . . . . . . . . . . . . . . Test of claim . .
School: Berkeley
Course: STATISTICS
Chapter 19: Sampling Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
School: Berkeley
Course: STATISTICS
Chapter 20: chance error in sampling Context 2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Population and parameter. . . . . . . . . . . . . . . . . . . . . . .
School: Berkeley
Course: STATISTICS
Chapter 21: accuracy of percentages Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Estimating the SE Example . . . . . . . . . Strategy. . . . . . . . . . Rea
School: Berkeley
Course: STATISTICS
Chapter 16: law of averages Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Law of averages Coin tossing experiment . Questions. . . . . . . . . . . First 50 t
School: Berkeley
Psych 133 Allison Harvey Section Friday 1 2 pm Hyunjoong Joo 23208055 Reaction Paper of Sleep and youth suicidal behavior: a neglected eld Sleep undergoes continuous changes during puberty and additionally, suicide risks begin to escalate during this peri
School: Berkeley
Course: Probability
Retention Factor (Rf)! Not a Physical Constant! Rf = ! distance to ! midpoint! of spot! distance to ! solvent front! Rf depends on:! u The stationary phase ! u The mobile phase ! u The amount of compound! spotted! u The temperature! TLC: Conclusions! Give
School: Berkeley
Course: Concepts Of Statistics
STAT 135: Linear Regression Joan Bruna Department of Statistics UC, Berkeley May 1, 2015 Joan Bruna STAT 135: Linear Regression Introduction: Example 1 We measure the Brain weight W (grams) and head size S (cubic cm) for 237 adults. (Source: R.J. Gladston
School: Berkeley
Course: Concepts Of Statistics
Paired Samples STAT 135: Distributions Derived From the Normal Joan Bruna Department of Statistics UC, Berkeley March 9, 2015 Joan Bruna STAT 135: Distributions Derived From the Normal Paired Samples Distributions derived from the normal distribution Joan
School: Berkeley
Course: Concepts Of Statistics
Logistics Introduction to Statistical Inference Elementary facts of probability Useful inequalities, LLN and CLT Introduction to Stat 135 Joan Bruna Department of Statistics UC, Berkeley January 21, 2015 Joan Bruna Introduction to Stat 135 Logistics Intro
School: Berkeley
Course: Concepts Of Statistics
Stats 135: Parameter Estimation Joan Bruna Department of Statistics UC, Berkeley February 6, 2015 Joan Bruna Stats 135: Parameter Estimation Introduction to statistical inference Joan Bruna Stats 135: Parameter Estimation Proportion of earth surface cover
School: Berkeley
Course: Concepts Of Statistics
Introduction to hypothesis testing Hypothesis Testing STAT 135: Intro to hypothesis testing Joan Bruna Department of Statistics UC, Berkeley March 11, 2015 Joan Bruna STAT 135: Intro to hypothesis testing Introduction to hypothesis testing Hypothesis Test
School: Berkeley
Course: STATISTICS
Stat 20 Quiz 1 February 10, 2014 Please write your name below and circle your section. Answer the questions in the space provided. There are questions on the back. This quiz covers material from Homeworks 1 a
School: Berkeley
Course: STAT 21
Quiz 1 Statistics 21 Spring 2010 Ibser 1. A large class takes a test, and the table shows their scores. For all parts of this problem, assume that the scores are continuous and that they are evenly distributed within each separate class interval. The maxi
School: Berkeley
Course: STAT 21
Quiz 1 Solutions Statistics 21 Spring 2010 Ibser Each part of every problem is worth 2 pts except 1a worth 3 and 1b worth 1. 1. (a) Interval Percent Height 10-50 20 0.5 50-70 28 1.4 70-80 20 2 80-90 22 2.2 90-100 10 1 Draw histogram with these axes: x axi
School: Berkeley
Course: STATISTICS
Stat20 Quiz2 February24,2014 Name:_Section:101, 102,103,104 105,106,107,108 SOLUTIONS?pointspossible Part1Forquestions12,showallworkandputaboxaroundyouranswer.Forquestion3,no workisrequired.UsetheprovidedNormalTableonthebackifneeded. 1. ForfreshmenatUCBer
School: Berkeley
Course: Statistics For Business Majors
Stat 21, Fall 2011, Murali-Stoyanov Quiz 2 (v1) Answer Key 1a) (70-79)/8.5 = -1.06 ~ -1.05. Area = 70.63% (85-79)/8.5 = 0.71 ~ 0.70. Area = 51.61% (70.63%/2) + (51.61%/2) = 61.12% 1b) 35th Percentile -> Area = 30% (82-79)/8.5 = 0.35. Area = 27.37% (30%/2)
School: Berkeley
Course: Probability
Stat 134: problems before the nal exam Michael Lugo May 6, 2011 Some problems recommended to do before the nal exam: 6.4.6, 6.4.9, 6.4.12, 6.4.21, 6.5.2, 6.5.4, 6.5.6, 6.5.8, 6.R.8(c), 6.R.13(b), 6.R.14, 6.R.18, 6.R.25 6.4.6 Let X1 and X2 be the numbers o
School: Berkeley
Course: Theoretical Statistics
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 5 - Solutions Fall 2008 Issued: Tuesday, September 29, 2009 Problem 5.1 First, notice that we can rewrite: p(x; ) = exp [x log log ( log(1 )] so p belongs
School: Berkeley
STAT516 Solution to Homework 2 1.4.5: a) Let U1=(urn 1 chosen), U2=(urn 2 chosen), B=(black ball chosen), W=(White ball chosen). 2/5 B 1/2 U1 3/5 4/7 W B 1/2 U2 3/7 W b) P(U1)=1/2=P(U2); P(W|U1)=3/5; P(B|U1)=2/5; P(W|U2)=3/7; P(B|U2)=4/7 c) P(B)=P(B|U1)P(
School: Berkeley
UC Berkeley Department of Electrical Engineering and Computer Science Department of Statistics EECS 281A / STAT 241A Statistical Learning Theory Solutions to Problem Set 3 Fall 2011 Issued: Monday, October 10, 2011 Due: Monday, October 24, 2011 Reading: F
School: Berkeley
Course: Probability
Homework 10 Solutions 5.2.4 Statistics 134, Pitman , Fall 2012 a) y x 6e2x3y dydx P (X x, Y y ) = 0 0 x = 0 y 1 6e2x ( e3y ) dx 3 0 x 2e2x dx = (1 e3y ) 0 3y = (1 e b) )(1 e2x ) 6e2x3y dy = 2e2x fX (x) = 0 c) 6e2x3y dx = 3e3y fY (y ) = 0 d) Yes, they are
School: Berkeley
Math 361/Stat 351 X1 Homework 10 Solutions Spring 2003 Graded problems: 1(d), 3(c), 4(b), 7 Problem 1. [4.2.4] Suppose component lifetimes are exponentially distributed with mean 10 hours. Find (a) the probability that a component survives 20 hou
School: Berkeley
Course: Theoretical Statistics
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 1 Fall 2007 Issued: Thursday, August 30 d p m.s. Due: Thursday, September 6 Notation: The symbols cfw_, , denote convergence in distribution, probability
School: Berkeley
Course: Concepts Of Statistics
STAT 135 Lab 7 Distributions derived from the normal distribution, and comparing independent samples. March 16, 2015 The 2 distribution The 2 distribution We have seen several instances of test statistics which follow a 2 distribution, for example, the ge
School: Berkeley
Course: Concepts Of Statistics
Lab 7 solutions STAT 135 Fall 2015 March 16, 2015 Exercise 1: Moment generating functions For each of the following distributions, calculate the moment generating function, and the rst two moments. 1. X P oisson() Recall that the moment generating functio
School: Berkeley
Course: Concepts Of Statistics
Lab 6 solutions STAT 135 Fall 2015 March 8, 2015 Exercise 1: Hypothesis testing and CI Duality Suppose that X1 = x1 , ., Xn = x1 , are such that Xi N (, and known. Show that the hypothesis test which tests 2 ) with unknown H0 : = 0 H1 : 6= 0 at signicance
School: Berkeley
Course: Concepts Of Statistics
STAT 135 Lab 6 Hypothesis Testing March 8, 2015 The duality between CI and hypothesis testing The duality between CI and hypothesis testing Recall that the acceptance region was the range of values of our test statistic for which H0 will not be rejected a
School: Berkeley
Course: Concepts Of Statistics
Exercise 1: Bootstrapping Suppose that a sample consists of the following observations: 78, 86, 97, 91, 83, 89, 92, 88, 79, 68 Then the -trimmed mean is the average of the inner (1 2) values in the sample. For example, if = 0.2, then the trimmed mean is t
School: Berkeley
Course: Concepts Of Statistics
STAT 135 Lab 5 Bootstrapping and Hypothesis Testing March 2, 2015 The Bootstrap Bootstrap Suppose that we are interested in estimating a parameter from some population with members x1 , ., xM , but that this population is so large that we cannot possibly
School: Berkeley
Course: Statistical Genomics
We conclude that Y1 and Y2 have covariance 2 2 Cov [Y1 , Y2 ] = CY (1, 2) = (1 2 ) sin cos . (4) Since Y1 and Y2 are jointly Gaussian, they are independent if and only if Cov[Y1 , Y2 ] = 0. 2 2 Thus, Y1 and Y2 are independent for all if and only if 1 = 2
School: Berkeley
Course: Statistical Genomics
(c) Y has correlation matrix RY = CY + Y Y = 1 43 55 8 + 0 9 55 103 8 0 = 1 619 55 9 55 103 (6) (d) From Y , we see that E[Y2 ] = 0. From the covariance matrix CY , we learn that Y2 has 2 variance 2 = CY (2, 2) = 103/9. Since Y2 is a Gaussian random varia
School: Berkeley
Course: Statistical Genomics
Problem 5.3.7 Solution (a) Note that Z is the number of three page faxes. In principle, we can sum the joint PMF PX,Y,Z (x, y, z) over all x, y to nd PZ (z). However, it is better to realize that each fax has 3 pages with probability 1/6, independent of a
School: Berkeley
Course: Statistical Genomics
Problem 5.5.2 Solution The random variable Jn is the number of times that message n is transmitted. Since each transmission is a success with probability p, independent of any other transmission, the number of transmissions of message n is independent of
School: Berkeley
Course: Statistical Genomics
Problem 5.6.4 Solution Inspection of the vector PDF f X (x) will show that X 1 , X 2 , X 3 , and X 4 are iid uniform (0, 1) random variables. That is, (1) f X (x) = f X 1 (x1 ) f X 2 (x2 ) f X 3 (x3 ) f X 4 (x4 ) where each X i has the uniform (0, 1) PDF
School: Berkeley
Course: Statistical Genomics
Problem 5.6.9 Solution Given an arbitrary random vector X, we can dene Y = X X so that CX = E (X X )(X X ) = E YY = RY . (1) It follows that the covariance matrix CX is positive semi-denite if and only if the correlation matrix RY is positive semi-denite.
School: Berkeley
Course: Concepts Of Probability
Statistics 134, Section 2, Spring 2010 Instructor: Hank Ibser Lectures: TTh 11-12:30 in 60 Evans. Oce Hours: TTh 9:30-10:30 and 3:40-4:30, in 349 Evans Hall. Other times/places by appt. Oce Phone: 642-7495 Email: hank@stat.berkeley.edu Text: Probability b
School: Berkeley
Course: Introductory Probability And Statistics For Busines
UNIVERSITY OF CALIFORNIA Department of Economics Econ 100B Course Outline Spring 2012 Economics 100B Economic Analysis: Macroeconomics Professor Steven A. Wood Administrative Detail: Class Sessions: Tuesdays and Thursdays, 3:30 p.m. 5:00 p.m., 2050 Valley
School: Berkeley
Course: Introductory Probability And Statistics For Busines
Statistics 21, Section 1, Spring 2012 Instructor: Hank Ibser Lectures: MWF 9-10, 155 Dwinelle Email: hank@stat.berkeley.edu Office Hours: MW 10:10-11, 1:10-2, in 349 Evans Hall. Text: Statistics, 4rd ed. by Freedman, Pisani, Purves, Well cover most of cha
School: Berkeley
Stat 150 Spring 2015 Syllabus Available online at http:/www.stat.berkeley.edu/~sly/Stat150Spring2015Syllabus.pdf Instructor: Allan Sly GSI: Jonathan Hermon Course Webpage: http:/www.stat.berkeley.edu/~sly/STAT150.html Class Time: MWF 12:00 - 1:00 PM in ro
School: Berkeley
Course: Concepts Of Probability
Stat 134: Concepts of Probability Instructor: Michael Lugo e-mail: mlugo at stat dot berkeley dot edu Office: 325 Evans Office hours: TBA GSI: TBA. Class schedule: Lectures Monday, Wednesday, and Friday, from 12:10 PM to 1:00 PM, 60 Evans. There are two o
School: Berkeley
Course: Concepts In Computing With Data
STAT$133:$Concepts$in$Computing$with$Data$ ! $ Instructor:$Deborah!Nolan,!395!Evans,$ deborah_nolan@berkeley.edu! OH:$Wed!1:30>3:30! $ GSI:!Bradly,!Christine,!Inna! OH:!Mon!10>11,!5>6,!Tue!2>4,!Wed!4>5,!and!Thu!5>7$ ! Lectures:!Tue/Thu!12:30>2pm;!2050!VLS
School: Berkeley
Course: STATISTICS
Stat 20 Quiz 1 February 10, 2014 Please write your name below and circle your section. Answer the questions in the space provided. There are questions on the back. This quiz covers material from Homeworks 1 a
School: Berkeley
Course: Theoretical Statistics
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 5 - Solutions Fall 2008 Issued: Tuesday, September 29, 2009 Problem 5.1 First, notice that we can rewrite: p(x; ) = exp [x log log ( log(1 )] so p belongs
School: Berkeley
Course: STAT 21
Quiz 1 Statistics 21 Spring 2010 Ibser 1. A large class takes a test, and the table shows their scores. For all parts of this problem, assume that the scores are continuous and that they are evenly distributed within each separate class interval. The maxi
School: Berkeley
Course: Probability
Retention Factor (Rf)! Not a Physical Constant! Rf = ! distance to ! midpoint! of spot! distance to ! solvent front! Rf depends on:! u The stationary phase ! u The mobile phase ! u The amount of compound! spotted! u The temperature! TLC: Conclusions! Give
School: Berkeley
STAT516 Solution to Homework 2 1.4.5: a) Let U1=(urn 1 chosen), U2=(urn 2 chosen), B=(black ball chosen), W=(White ball chosen). 2/5 B 1/2 U1 3/5 4/7 W B 1/2 U2 3/7 W b) P(U1)=1/2=P(U2); P(W|U1)=3/5; P(B|U1)=2/5; P(W|U2)=3/7; P(B|U2)=4/7 c) P(B)=P(B|U1)P(
School: Berkeley
UC Berkeley Department of Electrical Engineering and Computer Science Department of Statistics EECS 281A / STAT 241A Statistical Learning Theory Solutions to Problem Set 3 Fall 2011 Issued: Monday, October 10, 2011 Due: Monday, October 24, 2011 Reading: F
School: Berkeley
Course: Probability
Homework 10 Solutions 5.2.4 Statistics 134, Pitman , Fall 2012 a) y x 6e2x3y dydx P (X x, Y y ) = 0 0 x = 0 y 1 6e2x ( e3y ) dx 3 0 x 2e2x dx = (1 e3y ) 0 3y = (1 e b) )(1 e2x ) 6e2x3y dy = 2e2x fX (x) = 0 c) 6e2x3y dx = 3e3y fY (y ) = 0 d) Yes, they are
School: Berkeley
Course: STAT 21
Quiz 1 Solutions Statistics 21 Spring 2010 Ibser Each part of every problem is worth 2 pts except 1a worth 3 and 1b worth 1. 1. (a) Interval Percent Height 10-50 20 0.5 50-70 28 1.4 70-80 20 2 80-90 22 2.2 90-100 10 1 Draw histogram with these axes: x axi
School: Berkeley
Course: Probability
Homework 6 Problems Statistics 134, Pitman , Fall 2012 3.4.4 In the game of odd one out three people each toss a fair coin to see if one of their coins shows a dierent face from the other two. 1. After one play, what is the probability of some person bein
School: Berkeley
Course: STATISTICS
Stat20 Quiz2 February24,2014 Name:_Section:101, 102,103,104 105,106,107,108 SOLUTIONS?pointspossible Part1Forquestions12,showallworkandputaboxaroundyouranswer.Forquestion3,no workisrequired.UsetheprovidedNormalTableonthebackifneeded. 1. ForfreshmenatUCBer
School: Berkeley
Course: Statistics For Business Majors
Stat 21, Fall 2011, Murali-Stoyanov Quiz 2 (v1) Answer Key 1a) (70-79)/8.5 = -1.06 ~ -1.05. Area = 70.63% (85-79)/8.5 = 0.71 ~ 0.70. Area = 51.61% (70.63%/2) + (51.61%/2) = 61.12% 1b) 35th Percentile -> Area = 30% (82-79)/8.5 = 0.35. Area = 27.37% (30%/2)
School: Berkeley
Math 361/Stat 351 X1 Homework 10 Solutions Spring 2003 Graded problems: 1(d), 3(c), 4(b), 7 Problem 1. [4.2.4] Suppose component lifetimes are exponentially distributed with mean 10 hours. Find (a) the probability that a component survives 20 hou
School: Berkeley
Lab 2 Solutions Stat 135 Tessa Childers-Day March 3, 2011 1 Chapter 8, Problem 43 Please note that I was very specific of the format of the report. I posted an example report, and noted several times that the code was to be printed separately from the ans
School: Berkeley
Course: Probability
Stat 134: problems before the nal exam Michael Lugo May 6, 2011 Some problems recommended to do before the nal exam: 6.4.6, 6.4.9, 6.4.12, 6.4.21, 6.5.2, 6.5.4, 6.5.6, 6.5.8, 6.R.8(c), 6.R.13(b), 6.R.14, 6.R.18, 6.R.25 6.4.6 Let X1 and X2 be the numbers o
School: Berkeley
Course: Probability
Homework 9 Problems Statistics 134, Pitman , Fall 2012 4.5.4 Let X be a random variable with c.d.f. F (x). Find the c.d.f. of aX + b rst for a > 0, then for a < 0. 4.5.6 Let X be a random variable with c.d.f. F (x) = x3 for 0 x 1. Find: 1. P (X 1 ); 2 2.
School: Berkeley
Course: Theoretical Statistics
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 1 Fall 2007 Issued: Thursday, August 30 d p m.s. Due: Thursday, September 6 Notation: The symbols cfw_, , denote convergence in distribution, probability
School: Berkeley
Course: Intro To Probability And Statistics
Statistics 20: Midterm Solutions Summer Session 2007 1. [20 points] Pressure and Boiling Points. (a) [5 points] What is the equation of the regression line for predicting P RES from T EMP ? Solution: Here the x variable is TEMP in Fahrenheit and the y var
School: Berkeley
Course: Intro To Probability And Statistics
Statistics 20: Summer Session 2007 Quiz n. 1 Friday July 6, 2007 Full Name (Please print): ID: Lab: YOU MUST SHOW WORK TO RECEIVE ANY CREDIT 1. The British government conducts regular surveys of household spending. The average weekly household spending on
School: Berkeley
Course: STAT 21
Quiz 2 Statistics 21 Spring 2010 Ibser 1.)Suppose we have two sets of data A and B. a) Compute the correlation of X and Y of set A. b) Is there any number that could be put in the blank in set B which would make the correlation between X and Y equal to ze
School: Berkeley
Course: 135
Stat 135, Fall 2011 HOMEWORK 8 due WEDNESDAY 11/9 at the beginning of lecture Friday 11/11 is a holiday, so this is a very short homework due two days earlier at the start of lecture. Grading: A (4 points) for all three problems done well, B (2 points) fo
School: Berkeley
Statistics 20: Quiz 4 Solutions 1. A team of doctors want to estimate the life expectancy of students afflicted with the rare genetic disease statinotisticitis; however, only 15 known cases have ever been diagnosed. The sample reported a mean lifespa
School: Berkeley
Statistics 20: Quiz 1 Solutions Speed (mph) 0-10 10-20 20-40 40-80 80-95 Percentage of Total Cars 20 10 40 20 10 The above table depicts data collected in a (hypothetical) survey studying the distribution of traffic speed on the Bay Bridge. Each gro
School: Berkeley
UC Berkeley Department of Electrical Engineering and Computer Science Department of Statistics EECS 281A / STAT 241A Statistical Learning Theory Problem Set 5 Fall 2011 Issued: Thursday, November 10, 2011 Due: Wednesday, November 30, 2011 Problem 5.1 Conv
School: Berkeley
Course: 135
Stat 135, Fall 2011 A. Adhikari HOMEWORK 4 (due Friday 9/30) 1. 8.20. Use R to do this one accurately. Be careful about constants when youre working out the distribution of 2 . 2. 8.32. You dont have to do all six intervals in parts (b) and (c); just do t
School: Berkeley
Course: STATISTICS
Stat 20 Quiz 3 March 10, 2014 Name:_Section:101,102,103,104 105,106,107,108 1.Astatisticsclassisunhappywithitsmidtermperformance.Theclassmanagestopersuadetheprofessortogiveallthe studentstheopportunitytotakearetest.Twoscoreswillbepositivelyandlinearlycorr
School: Berkeley
Course: Probability
Homework 10 Problems Statistics 134, Pitman , Fall 2012 5.2.4 For random variables X and Y with joint density function f (x, y ) = 6e2x3y (x, y > 0) and f (x, y ) = 0 otherwise, nd: 1. P (X x, Y y ); fX (x); fY (y ). 2. Are X and Y independent? Give a rea
School: Berkeley
Course: 135
Stat 135, Fall 2011 A. Adhikari HOMEWORK 5 (due Friday 10/7) 1. 9.11. Use R to do the plots accurately. In each case, say what the limiting power is as approaches 0. 2. 9.12. 3. 9.13. In c, use R to nd the critical values x0 and x1 . Turn the page for d.
School: Berkeley
UC Berkeley Department of Electrical Engineering and Computer Science Department of Statistics EECS 281A / STAT 241A Statistical Learning Theory Problem Set 3 Fall 2011 Issued: Monday, October 10, 2011 Due: Monday, October 24, 2011 Reading: For this probl
School: Berkeley
Course: Introduction To Time Series
Homework 2 solutions Joe Neeman September 22, 2010 1. (a) We compute three cases: since the Wt are uncorrelated, we can ignore any cross-terms of the form EWs Wt when s = t. Then 9 19 25 EWt2 1 + EWt2 2 = 4 4 2 15 5 5 (1) = EWt2 + EWt2 1 = 2 4 4 3 3 (2
School: Berkeley
Course: Theoretical Statistics
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 8 Fall 2006 Issued: Thursday, October 26, 2006 Due: Thursday, November 2, 2006 Some useful notation: The pth quantile of a continuous random variable with
School: Berkeley
Course: Probability
Homework # 2 Statistics 134, Pitman , Spring 2009 2.1.2 P (2 boys and 2 girls) = 4 (1/2)4 = 6/24 = 0.375 < 0.5. So families with dierent 2 numbers of boys and girls are more likely than those having an equal number of boys and girls, and the relative freq
School: Berkeley
School: Berkeley
Course: Introductory Probability And Statistics For Busines
- Home | Text Table of Contents | Assignments | Calculator | Tools | Review | Glossary | Bibliography | System Requirements | Author's Homepage Chapter 21 Testing Equality of Two Percentages Chapter 19, "Hypothesis Testing: Does Chance Explain the Results
School: Berkeley
UC Berkeley Department of Electrical Engineering and Computer Science Department of Statistics EECS 281A / STAT 241A Statistical Learning Theory Problem Set 1 Fall 2011 Issued: Thurs, September 8, 2011 Due: Monday, September 19, 2011 Reading: For this pro
School: Berkeley
UGBA 103, Midterm Exam: March 05, 2012 Name: ID: Section: The answers on this midterm are entirely my own work. I neither gave nor received any aid while taking this midterm. _ Signature Please remember to write your name legibly on every page. The maximu
School: Berkeley
UC Berkeley Department of Electrical Engineering and Computer Science Department of Statistics EECS 281A / STAT 241A Statistical Learning Theory Solutions to Problem Set 1 Fall 2011 Issued: Thurs, September 8, 2011 Due: Monday, September 19, 2011 Reading:
School: Berkeley
Course: 135
Stat 135, Fall 2011 HOMEWORK 1 (due Friday 9/9) 1a) Let x1 , x2 , . . . , xn be a list of numbers with mean and SD . Show that 2 = 1 n n x2 2 i i=1 b) A class has two sections. Students in Section 1 have an average score of 75 with an SD of 8. Students in
School: Berkeley
Course: PROBABILITY AND STATISTICS FOR BUSINESS
Statistics 21, Summation and Correlation The correlation coefficient r can be written either 1 n (xi - x) (yi - y ) n i=1 SDx SDy The proof is as follows: 1 n (xi - x) (yi - y ) n i=1 SDx SDy = = = = 1 n SDx SDy 1 SDx SDy 1 n n i=1 n i=1 or
School: Berkeley
Course: Concepts Of Probability
Statistics 134, Section 2, Spring 2010 Instructor: Hank Ibser Lectures: TTh 11-12:30 in 60 Evans. Oce Hours: TTh 9:30-10:30 and 3:40-4:30, in 349 Evans Hall. Other times/places by appt. Oce Phone: 642-7495 Email: hank@stat.berkeley.edu Text: Probability b
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Math 4653: Elementary Probability: Spring 2007 Homework #6. Problems and Solutions 1. Sec. 4.2: #6: A Geiger counter is recording background radiation at an average rate of one hit per minute. Let T3 be the time in minutes when the third hit occurs after
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Math 4653: Elementary Probability: Spring 2007 Homework #1. Problems and Solutions 1. Appendix 1 (vi): Prove that 2n n n = k=0 n k n n-k n = k=0 n k 2 . Solution. The left side is the number of all subsets of the set cfw_1, 2, . . . , n-1, n, n+1, . . . ,
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Math 4653: Elementary Probability: Spring 2007 Homework #5. Problems and Solutions 1. Sec. 3.5: #2: How many raisins must cookies contain on average for the chance of a cookie containing at least one raisin to be at least 99%? Solution. Let X be the numbe
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Course: Probability
Homework 8 Problems Statistics 134, Pitman , Fall 2012 4.2.4 Suppose component lifetimes are exponentially distributed with mean 10 hours. Find: 1. the probability that a component survives 20 hours; 2. the median component lifetime; 3. the SD of componen
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Math 4653: Elementary Probability: Spring 2007 Homework #4. Problems and Solutions 1. Sec. 3.1: #8a): A hand of five cards contains two aces and three kings. The five cards are shuffled and dealt one by one, until an ace appears. Display in a table the di
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Math 361 X1 Homework 4 Solutions Spring 2003 Graded problems: 1(b)(d); 3; 5; 6(a); As usual, you have to solve the problems rigorously, using the methods introduced in class. An answer alone does not count. The problems in this assignment are inte
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Math 361 X1 Homework 6 Solutions Spring 2003 Graded problems: 2(a);4(a)(b);5(b);6(iii); each worth 3 pts., maximal score is 12 pts. Problem 1. [3.1:4] Let X1 and X2 be the numbers obtained on two rolls of a fair die. Let Y1 = max(X1 , X2 ) and Y2
School: Berkeley
Course: Introductory Probability And Statistics For Busines
UNIVERSITY OF CALIFORNIA Department of Economics Econ 100B Course Outline Spring 2012 Economics 100B Economic Analysis: Macroeconomics Professor Steven A. Wood Administrative Detail: Class Sessions: Tuesdays and Thursdays, 3:30 p.m. 5:00 p.m., 2050 Valley
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Course: Probability
Statistics 2 Problems from past nal exams 1. (5 points) The paragraph below is taken from an article in the San Francisco Chronicle of Tuesday, March 21, 1995. The person quoted in the article is Patrick Portway, executive director of the United States Di
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Math 361 X1 Homework 9 Solutions Spring 2003 Graded problems: 1(a), 2, 4(b), 5(b) (3 points each - 12 points maximal); 7 (Bonus problem): up to 2 additional points Problem 1. [4.R:25, variant] Suppose U is distributed uniformly on the interval (0
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Math 4653: Elementary Probability: Spring 2007 Homework #3. Problems and Solutions 1. Sec. 2.4: #2: Find Poisson approximations to the probabilities of the following events in 500 independent trials with probability 0.02 of success on each trial: a) 1 suc
School: Berkeley
Course: Introductory Probability And Statistics For Busines
Statistics 21, Section 1, Spring 2012 Instructor: Hank Ibser Lectures: MWF 9-10, 155 Dwinelle Email: hank@stat.berkeley.edu Office Hours: MW 10:10-11, 1:10-2, in 349 Evans Hall. Text: Statistics, 4rd ed. by Freedman, Pisani, Purves, Well cover most of cha
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STAT 20 - Fall 2011 - Practice Midterm 1 Most explanations require just a sentence or two. On calculations, show your work and work through to a numerical answers, upto at least 2 decimal places. 1. Below are the statistics of 3 lists of numbers. The aver
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Math 4653: Elementary Probability: Spring 2007 Homework #7. Problems and Solutions 1. Ch. 4, Review: #21: Suppose R1 and R2 are two independent random variables with the 1 same density function f (x) = x exp(- 2 x2 ) for x 0. Find a) the density of Y = mi
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Math 361 X1 Homework 8 Solutions Spring 2003 Graded problems: 1, 4(b), 5, 6; 3 points each, 12 points total Problem 1. In a certain math class each homework problem is scored on a 0 3 point scale. A lazy grader decides to grade these problems by
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Math 361 X1 Homework 1 Solutions Spring 2003 Graded problems: 1; 2(b);3;5; each worth 3 pts., maximal score is 12 pts. Problem 1. A coin is tossed repeatedly. What is the probability that the second head appears at the 5th toss? (Hint: Since only
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Math 4653: Elementary Probability: Spring 2007 Homework #2. Problems and Solutions (corrected) 1. Sec. 1.5: #2: Polyas urn scheme. An urn contains 4 white balls and 6 black balls. A ball is chosen at random, and its color noted. The ball is then replaced,
School: Berkeley
Course: Concepts Of Statistics
STAT 135 Lab 7 Distributions derived from the normal distribution, and comparing independent samples. March 16, 2015 The 2 distribution The 2 distribution We have seen several instances of test statistics which follow a 2 distribution, for example, the ge
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Course: Concepts Of Statistics
Lab 7 solutions STAT 135 Fall 2015 March 16, 2015 Exercise 1: Moment generating functions For each of the following distributions, calculate the moment generating function, and the rst two moments. 1. X P oisson() Recall that the moment generating functio
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Course: Concepts Of Statistics
Lab 6 solutions STAT 135 Fall 2015 March 8, 2015 Exercise 1: Hypothesis testing and CI Duality Suppose that X1 = x1 , ., Xn = x1 , are such that Xi N (, and known. Show that the hypothesis test which tests 2 ) with unknown H0 : = 0 H1 : 6= 0 at signicance
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Course: Concepts Of Statistics
STAT 135 Lab 6 Hypothesis Testing March 8, 2015 The duality between CI and hypothesis testing The duality between CI and hypothesis testing Recall that the acceptance region was the range of values of our test statistic for which H0 will not be rejected a
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Course: STATISTICS
Chapter 23: accuracy of averages Context: previous chapters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Context: previous chapters . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
School: Berkeley
Course: STATISTICS
Chapter 26: tests of significance Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Tax revenue example Example . . . . . . . . . . . . . . . . Test of claim . .
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Course: STATISTICS
Chapter 19: Sampling Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Course: STATISTICS
Chapter 20: chance error in sampling Context 2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Population and parameter. . . . . . . . . . . . . . . . . . . . . . .
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Course: STATISTICS
Chapter 21: accuracy of percentages Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Estimating the SE Example . . . . . . . . . Strategy. . . . . . . . . . Rea
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Course: STATISTICS
Chapter 16: law of averages Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Law of averages Coin tossing experiment . Questions. . . . . . . . . . . First 50 t
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Course: STATISTICS
Chapter 11: r.m.s. error for regression Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Prediction error r.m.s. error for the regression line 68% 95% rule . .
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Course: STATISTICS
Chapter 17: expected value and standard error for the sum of the draws from a box Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 When we do this 10,000 times.
School: Berkeley
Course: STATISTICS
Chapter 10: Regression Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Regression line Graph of averages . . Regression estimate . Example . . . . . . . . Regr
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Course: STATISTICS
Chapter 18: probability histograms and the central limit theorem Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Probability histograms 3 Probability histogram
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Course: STATISTICS
Chapter 9: More correlation Features of r r has no units. . . . . . . . . . . . Change of scale. . . . . . . . . . . Changing the order of x and y Changing SDs. . . . . . . . . . . . When to use r? . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
School: Berkeley
Course: STATISTICS
Chapter 2: Observational studies Last chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 New chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
School: Berkeley
Course: STATISTICS
Chapter 1: Controlled experiments Outline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Acne drug Background . . . . . . . . . . . . Questions about background . Qu
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Course: STATISTICS
Chapter 4: Average and standard deviation Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Average vs. median 3 Average . . . . . . . . . . . . . . . . . . . .
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Course: STATISTICS
Chapter 8: Correlation Context . . . . . . . . . . . . . . . . . . . . . Association . . . . . . . . . . . . . . . . . . . Dependent and independent variables . Summarizing data on two variables. . . Interpreting r . . . . . . . . . . . . . . . . . Values
School: Berkeley
Course: STATISTICS
Chapter 5: The normal approximation for data Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Normal curve 3 Normal curve . . . . . . . . . . . . . . . . . . .
School: Berkeley
Course: STATISTICS
Chapter 3: Histograms Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Histograms Histogram . . . . . . . . . . Drawing a histogram . . . Histogram: main points
School: Berkeley
Course: Concepts Of Probability
Stat 134 Fall 2011: Notes on generating functions Michael Lugo October 14, 2011 1 Denitions Given a random variable X which always takes on a positive integer value, we dene the probability generating function fX (z) = P (X = 0) + P (X = 1)z + P (X = 2)z
School: Berkeley
Course: Concepts Of Probability
Stat 134 Fall 2011: The expectation of the maximum of exponentials Michael Lugo October 28, 2011 Let X1 , . . . , Xn be independent random variables, each exponential with rate 1. We found in class that the CDF of their maximum, X = max(X1 , . . . , Xn ),
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Course: Concepts Of Probability
Stat 134 Fall 2011: Conditioning on events of probability zero Michael Lugo November 14, 2011 1 Order statistics In class on Wednesday, November 9, we saw the following example: let U1 , U2 , U3 , U4 be four independent uniform(0,1) random variables. Let
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Course: Concepts Of Probability
Stat 134 Fall 2011: correlation between order statistics Michael Lugo December 4, 2011 In class on Friday, we saw the following example: let U1 , . . . , U5 be independent random variables, each uniformly distributed on [0, 1]. Let X = U(2) and Y = U(4) .
School: Berkeley
Course: Concepts Of Probability
Stat 134 Fall 2011: Distributions of numbers of children Michael Lugo November 16, 2011 We considered the following model in class today: in a certain town, the probability that a random family has t children is P (T = t) = (1 p)t p. All children have pro
School: Berkeley
Course: Concepts Of Probability
Stat 134 Fall 2011: Stirlings formula Michael Lugo September 14, 2011 Stirlings approximation to the factorial is n n! 2n e n . The symbol has a technical meaning: if we write f (n) g(n) for two functions f and g, we mean that limn f (n)/g(n) = 1. Dene p(
School: Berkeley
Course: Concepts Of Probability
Stat 134 Fall 2011: a proof of the central limit theorem Michael Lugo November 14, 2011 In Section 5.3, Pitman proves that if X N (, 2 ) and Y N (, 2 ) and X and Y are independent, then X + Y N ( + , 2 + 2 ) by a geometric argument. This is a nice argumen
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Course: Concepts Of Probability
Stat 134 Fall 2011: A note on 6/ 2 Michael Lugo September 9, 2011 Attention conservation notice: this note is devoted to proving some of the parenthetical comments I made after the question about random integers on the homework. You dont need to read this
School: Berkeley
Course: Concepts Of Probability
Basic Distributions There are many probability distributions which can be described mathematically, that offer good descriptions of real world phenomena. We will study only a handful in this class. One very important property of distributions is that all
School: Berkeley
Course: Concepts Of Probability
Introduction to Poisson Regression As usual, we start by introducing an example that will serve to illustrative regression models for count data. We then introduce the Poisson distribution and discuss the rationale for modeling the logarithm of the mean a
School: Berkeley
Course: Statistical Genomics
and covariance matrix CY = Var[Y ] = AC X A 4 2 1 1/3 2 4 2 1/3 = 2 = 1/3 1/3 1/3 3 1 2 4 1/3 Thus Y is a Gaussian (6, (3) (4) 2/3) random variable, implying 46 Y 6 > =1 P [Y > 4] = P 2/3 2/3 ( 6) = ( 6) = 0.9928 (5) Problem 5.8.2 Solution (a) The cova
School: Berkeley
Course: Statistical Genomics
function w=wrv1(lambda,mu,m) %Usage: w=wrv1(lambda,mu,m) %Return m samples of W=Y/X %X is exponential (lambda) %Y is exponential (mu) x=exponentialrv(lambda,m); y=exponentialrv(mu,m); w=y./x; function w=wrv2(lambda,mu,m) %Usage: w=wrv1(lambda,mu,m) %Retur
School: Berkeley
Course: Statistical Genomics
(b) For n = 3, 1 P min X i 3/4 = P min X i > 3/4 i (5) i = P [X 1 > 3/4, X 2 > 3/4, X 3 > 3/4] 1 1 1 3/4 3/4 (6) 3/4 3 = d x1 d x2 d x3 (7) = (1 3/4) = 1/64 (8) Thus P[mini X i 3/4] = 63/64. Problem 5.2.1 Solution This problem is very simple. In terms of
School: Berkeley
Course: Statistical Genomics
The condition Aw = 0 implies A 1 ACX Av+Av = 0 . 0 (4) This implies AA v + AA v = 0 AC1 Av + AC1 A v = 0 X (5) (6) X Since AA = 0, Equation (5) implies that AA v = 0. Since A is rank m, AA is an m m rank m matrix. It follows that v = 0. We can the
School: Berkeley
Course: Statistical Genomics
Following similar steps, one can show that f X 2 (x2 ) = 0 22x2 0 x2 0, otherwise. (6) f X (x) d x1 d x2 = 33x3 0 x3 0, otherwise. (7) 0 f X 3 (x3 ) = f X (x) d x1 d x3 = 0 0 Thus f X (x) = f X 1 (x1 ) f X 2 (x2 ) f X 3 (x3 ) . (8) We conclude that X 1 ,
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Course: Statistical Genomics
The covariance matrix of W is CW = E (W W )(W W ) =E X X Y Y (X X ) = E (X X )(X X ) E (Y Y )(X X ) = (2) (Y Y ) (3) E (X X )(Y Y ) E (Y Y )(Y Y ) (4) CX CXY . CYX CY (5) The assumption that X and Y are independent implies that CXY = E (X X )(Y Y ) = (E (
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1 MCMC Markov chain Monte Carlo or MCMC gives a exible way of sampling from complicated distributions. The idea is to take a high dimensional distribution in Rn (or some other space) and construct a Markov chain whose stationary distribution is (for conve
School: Berkeley
Course: Concepts In Computing With Data
R Markdown Reference Guide Learn more about R Markdown at rmarkdown.rstudio.com Learn more about Interactive Docs at shiny.rstudio.com/articles Syntax Contents: 1. Markdown Syntax 2. Knitr chunk options 3. Pandoc options Becomes Plain text ! End a line wi
School: Berkeley
Course: Concepts In Computing With Data
2/19/2015 Google's R Style Guide Google's R Style Guide R is a high-level programming language used primarily for statistical computing and graphics. The goal of the R Programming Style Guide is to make our R code easier to read, share, and verify. The ru
School: Berkeley
Course: Concepts In Computing With Data
2/6/15 What do you think of this plot? Lets x it! Making good plots is an iteraFve process Goal is to convey a message as clearly as possible FIND 5 things that you would change Visit the website hLp:/www
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Course: Concepts In Computing With Data
2/11/15 Add more data Add legend for dierent informa4on Add reference lines for important dates Graphics - Recap Data Stand Out Avoid having other graph elements interfere with data Use visually prominen
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Course: Concepts In Computing With Data
3/10/15 Shell Command Syntax UNIX command -options arg1 arg2! Blanks and are delimiters The number of arguments may vary. An argument comes at the end of the command line. Its usually the name of a le o
School: Berkeley
Course: Concepts In Computing With Data
1/20/15 Theme Sta$s$cs 133: Concepts in Compu$ng with Data Instructor: Deborah Nolan GSI: Bradley, Chris?ne, Inna Theme Use the computer expressively to conduct sta?s?cal analysis of data Use exis?ng soHware rath
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Course: Concepts In Computing With Data
3/9/15 Actually, it doesnt R uses a pseudo random number generator: How does R generate random numbers? It starts with a seed and an algorithm (i.e. a funcDon) The seed is plugged into the algorithm and a num
School: Berkeley
Course: Concepts In Computing With Data
3/9/15 Last 7me we saw how the computer represents plain text ASCII 0010 0011 0010 0100 Unicode 0000 0000 0010 0011 0000 0000 0010 0100 A a Files plain text and others Glyph # $ 0100 0001 0110 0001
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Course: Concepts In Computing With Data
2/26/15 Probability Simulation Probability allows us to quan5fy statements about the chance of an event taking place. For example - Flip a fair coin 1. Whats the chance it lands heads? 2. Flip it 4 5mes, wha
School: Berkeley
Course: Concepts In Computing With Data
2/26/15 Environments and Scope Global Environment 2 2 2 x z 17 lookAt = function(x)cfw_ y=3 print(x) print(y) print(z) lookAt function's Frame x 0 0 When you call a function, R creates a new workspace containing just the variables dened by the argume
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Course: Concepts In Computing With Data
2/24/15 More on Functions Write code in a plain text le, e.g. in a script in Rstudio source() code into R (do not copy and paste) Syntax error will be caught and line number given Line numbers may not locate
School: Berkeley
Course: Concepts In Computing With Data
2/19/15 Steps In Writing a Function Concrete: Start with code that addresses a problem with specic data Abstract: Change the code to refer to general variables rather than your specic data Encapsulate: Wrap the code into a function where the par
School: Berkeley
Course: Concepts In Computing With Data
2/4/15 Skills for a Data Scien8st Graphics Word Clouds are very popular elasticsearchpandas json postgres cloudera map ruby microsoft weka dashboard solr nosql java spss hbase mcmc oracle Name some concerns with this plot lisp
School: Berkeley
Course: Concepts In Computing With Data
2/18/15& Writing your own functions! Steps In Writing a Function ! Concrete: Start with code that addresses a problem with specic data! Abstract: Change the code to refer to general variables rather than your specic data! Encapsulate: Wrap the code int
School: Berkeley
Course: Concepts In Computing With Data
2/12/15 Reading data into R Data frames, Lists, Matrices Many data sets are stored in text les. The easiest way to read these into R is using either the read.table or read.csv func=on, both of which return
School: Berkeley
Course: Concepts In Computing With Data
1/20/15 Sta$s$cs 133: Ge-ng Started with R Why ? Why ? Some of you may have used sta6s6cal so9ware with a GUI, like Minitab or SPSS. You may also
School: Berkeley
Course: Concepts In Computing With Data
2/1/15 Suppose we want the: Subse+ng BMI of the 10th person in the family > @mi[10] Subset by posi,on [1] 30.04911 Ages of all but the rst person in the family > fage[-1] [1] 33 79 47 27 33 67 52 59 2
School: Berkeley
Course: Concepts In Computing With Data
2/1/15 The Family Data Frames > family! firstName gender age height weight bmi overWt! 1 Tom m 77 70 175 25.16239 TRUE! 2 May f 33 64 125 21.50106 FALSE! 3 Joe m 79 73 185 24.45884 FALSE! 4 Bob m 47 67 156 24.48414 FALSE! 5 Sue f 27 64 105 18.0608
School: Berkeley
Course: Concepts In Computing With Data
1/25/15 Sta:s:cians perspec:ve Data Types, Vectors, and Subse8ng Data Types R has a number of built-in data types. The three most basic types are numeric, character, and logical. You can check the type using t
School: Berkeley
Course: Concepts Of Probability
06/25 Tue 1.3: Distributions Intersection of Unions (Fact) A B C ( A B) C ( A C) ( B C ) n In general, P Ai An1 P Ai An1 . i 1 i 1 Union of Intersections (Fact) n A B C ( A B) C AC BC n n In general, P Ai An 1 P Ai An 1 . i 1 i 1 Mike Leong 06/
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Course: Concepts Of Probability
4 Continuous Distributions The basic ideas of previous sectiofis were the notions of a random variable, its probability distribution, expectation, and standard deviation. These ideas will now be extended from discrete distributions to continuous distribut
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Course: Concepts Of Probability
5 Continuous Joint Distributions The joint distribution of a pair of random variables X and Y is the probability distribution over the plane defined by P(B) = P(X, Y) E B) for subsets B of the plane. So P(B) is the probability that the random pair (X, Y)
School: Berkeley
Course: Concepts Of Probability
6 Dependence This chapter treats features of a joint distribution which give insight into the nature of dependence between random variables. Sections 6.1 and 6.2 concern conditional distributions and expectations in the discrete case. Then parallel formul
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Course: Concepts Of Probability
1 Introduction This chapter introduces the basic ,:oncepts of probability theory. These are the notions of: an outcome space, or set of all possible outcomes of some kind; events represented mathematically as subsets of an outcome space; and probability a
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Course: Concepts Of Probability
Distribution - - - - - - Summaries 476 Distribution Summaries Discrete name and range P(k) = P(X = k) for k E range mean vanance uniform on cfw_a, a + L, , , ,b 1 b-a+1 - a+b 2 (b-a+1)2-1 12 Bernoulli (p) on cfw_a, I P(l) =p: P(O) = 1- p p p(l- p) binomia
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Psych 133 Allison Harvey Section Friday 1 2 pm Hyunjoong Joo 23208055 Reaction Paper of Sleep and youth suicidal behavior: a neglected eld Sleep undergoes continuous changes during puberty and additionally, suicide risks begin to escalate during this peri
School: Berkeley
Course: Probability
Retention Factor (Rf)! Not a Physical Constant! Rf = ! distance to ! midpoint! of spot! distance to ! solvent front! Rf depends on:! u The stationary phase ! u The mobile phase ! u The amount of compound! spotted! u The temperature! TLC: Conclusions! Give
School: Berkeley
Course: Concepts Of Statistics
STAT 135: Linear Regression Joan Bruna Department of Statistics UC, Berkeley May 1, 2015 Joan Bruna STAT 135: Linear Regression Introduction: Example 1 We measure the Brain weight W (grams) and head size S (cubic cm) for 237 adults. (Source: R.J. Gladston
School: Berkeley
Course: Concepts Of Statistics
Paired Samples STAT 135: Distributions Derived From the Normal Joan Bruna Department of Statistics UC, Berkeley March 9, 2015 Joan Bruna STAT 135: Distributions Derived From the Normal Paired Samples Distributions derived from the normal distribution Joan
School: Berkeley
Course: Concepts Of Statistics
Logistics Introduction to Statistical Inference Elementary facts of probability Useful inequalities, LLN and CLT Introduction to Stat 135 Joan Bruna Department of Statistics UC, Berkeley January 21, 2015 Joan Bruna Introduction to Stat 135 Logistics Intro
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Course: Concepts Of Statistics
Stats 135: Parameter Estimation Joan Bruna Department of Statistics UC, Berkeley February 6, 2015 Joan Bruna Stats 135: Parameter Estimation Introduction to statistical inference Joan Bruna Stats 135: Parameter Estimation Proportion of earth surface cover
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Course: Concepts Of Statistics
Introduction to hypothesis testing Hypothesis Testing STAT 135: Intro to hypothesis testing Joan Bruna Department of Statistics UC, Berkeley March 11, 2015 Joan Bruna STAT 135: Intro to hypothesis testing Introduction to hypothesis testing Hypothesis Test
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Course: Concepts Of Statistics
STAT 135: Anova Joan Bruna Department of Statistics UC, Berkeley April 10, 2015 Joan Bruna STAT 135: Anova Motivation Say you want to buy a pair of shoes. You go to a store and observe a large sample of shoes with varying price. Where does the variance in
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Course: Concepts Of Statistics
Paired Samples STAT 135: Comparing two Samples Joan Bruna Department of Statistics UC, Berkeley March 16, 2015 Joan Bruna STAT 135: Comparing two Samples Paired Samples Comparing Independent Samples Joan Bruna STAT 135: Comparing two Samples Paired Sample
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Course: Concepts Of Statistics
Stats 135: E ciency and Su ciency Joan Bruna Department of Statistics UC, Berkeley February 13, 2015 Joan Bruna Stats 135: E ciency and Su ciency Su ciency (X1 , . . . , Xn ): n-dimensional; might be complicated/expensive to store Question: is there funct
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Course: Concepts Of Statistics
Stats 135: E ciency and Su ciency Joan Bruna Department of Statistics UC, Berkeley February 8, 2015 Joan Bruna Stats 135: E ciency and Su ciency Cramer-Rao lower bound This result basically states that the price to pay for having an unbiased estimator is
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Course: Concepts Of Statistics
Elementary facts of Probability Useful Probability Distributions Useful inequalities, LLN and CLT Probability Reminders for Stats 135 Joan Bruna Department of Statistics UC, Berkeley January 26, 2015 Joan Bruna Probability Reminders for Stats 135 Elementa
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Course: Concepts Of Statistics
Multiple regression Lung Capacity Example Binary Predictors Multiple Regression Daniel Turek STAT110 Summer School 12 February 2013 Full Example Summary Multiple regression Lung Capacity Example Binary Predictors Full Example Summary Introduction Simple l
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Course: Concepts Of Statistics
Variables Analysis of Covariance Logistic Regression Variables, Covariance, and Logistic Regression Daniel Turek STAT110 Summer School 13 February 2013 Example Variables Analysis of Covariance Logistic Regression Example Introduction There are three way o
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Course: Concepts Of Statistics
2 -Test Example Summary Interpreting the OR 2 -Test, Simpsons Paradox Daniel Turek STAT110 Summer School 29 January 2013 Simpsons Paradox 2 -Test Example Summary Interpreting the OR What is Chi-Squared? Greek letter Chi: , which is pronounced as kai 2 is
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Course: Concepts Of Statistics
Two Factor Experiments Formula Notes Interaction Eect Two Factor Factorial Designs Daniel Turek STAT110 Summer School 5 February 2013 Summary Two Factor Experiments Formula Notes Interaction Eect TWO FACTOR FACTORIAL EXPERIMENTS Block factor is of little
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Course: Concepts Of Statistics
Two Factor ANOVA Example Notes Two Factor ANOVA Daniel Turek STAT110 Summer School 4 February 2013 Block Designs Summary Two Factor ANOVA Example Notes Block Designs Summary TWO FACTOR ANOVA Generalisation of paired t-test Second factor controlled by stud
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Course: Concepts Of Statistics
Relative Risk (RR) Attributable Risk (AR) Odds Ratio (OR) Contingency Tables Daniel Turek STAT110 Summer School 28 January 2013 Condence Intervals Summary Relative Risk (RR) Attributable Risk (AR) Odds Ratio (OR) Condence Intervals Contingency tables are
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Course: Concepts Of Statistics
Post ANOVA Analysis Assumptions Post ANOVA Analysis Daniel Turek STAT110 Summer School 31 January 2013 Summary Post ANOVA Analysis Assumptions Summary ANOVA TABLE SUMMARY ANOVA TABLE (full version) Source Mean Group Error Total SS n 2 y 2 c1 n1 df 1 c2 c2
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Course: Concepts Of Statistics
Tree Diagrams PPV, NPV Examples, Summary Random Variables Tree Diagrams, Random Variables Daniel Turek STAT110 Summer School 14 January 2013 Examples, Summary Tree Diagrams PPV, NPV Examples, Summary Random Variables Summary Conditional Probability Pr(A B
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Course: Concepts Of Statistics
Condence Intervals for Proportions Sample Size Calculation Dierence Between Two Proportions Condence Intervals: Proportions Daniel Turek STAT110 Summer School 22 January 2013 Summary Condence Intervals for Proportions Sample Size Calculation Dierence Betw
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Course: Concepts Of Statistics
Binomial Distribution Assumptions Examples, Summary Binomial Distribution Daniel Turek STAT110 Summer School 15 January 2013 p-Values Examples, Summary Binomial Distribution Assumptions Examples, Summary p-Values Binomial Distribution Arises when investig
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Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 21: Intro to Hypothesis Testing Tessa L. Childers-Day UC Berkeley 10 April 2014 Recap Natural Questions Hypothesis Testing Example Outline 1 Recap 2 Natural Questions 3 Hypothesis Testing 4 Example 2 /
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Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 23: Two Sample Testing Tessa L. Childers-Day UC Berkeley 17 April 2014 Recap Surveys Experiments Outline 1 Recap 2 Surveys 3 Experiments 2 / 29 Recap Surveys Experiments Recap: Hypothesis Testing Steps
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Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 22: Hypothesis Testing Tessa L. Childers-Day UC Berkeley 15 April 2014 Recap Examples Outline 1 Recap 2 Examples 2 / 16 Recap Examples Recap: Hypothesis Testing Steps in Hypothesis Testing: 1 State the
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Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 24: 2 Testing Tessa L. Childers-Day UC Berkeley 22 April 2014 Recap Test for Distribution Test for Independence Outline 1 Recap 2 Test for Distribution 3 Test for Independence 2 / 40 Recap Test for Dist
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Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 25: Pitfalls and Limits In Testing Tessa L. Childers-Day UC Berkeley 24 April 2014 Recap Interpreting Signicance Data Snooping Role of Model Questions Matter Outline 1 Recap 2 Interpreting Signicance 3
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Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 20: Condence Intervals for Averages Tessa L. Childers-Day UC Berkeley 8 April 2014 Recap Known Box Unknown Box SE Summary Outline 1 Recap 2 Known Box 3 Unknown Box 4 SE Summary 2 / 17 Recap Known Box Un
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Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 19: Condence Intervals for Percentages Tessa L. Childers-Day UC Berkeley 3 April 2014 Recap Unknown Box Condence Intervals Examples Outline 1 Recap 2 Unknown Box 3 Condence Intervals 4 Examples 2 / 19 R
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Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 19: Condence Intervals for Percentages Tessa L. Childers-Day UC Berkeley 3 April 2014 Recap Unknown Box Condence Intervals Examples Outline 1 Recap 2 Unknown Box 3 Condence Intervals 4 Examples 2 / 24 R
School: Berkeley
Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 18: Simple Random Sampling Tessa L. Childers-Day UC Berkeley 1 April 2014 Recap Simple Random Samples EV and SE Examples Outline 1 Recap 2 Simple Random Samples 3 EV and SE 4 Examples 2 / 24 Recap Simpl
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Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 17: Using the Normal Curve with Box Models Tessa L. Childers-Day UC Berkeley 20 March 2014 Todays Goals Probability Histograms Probability Histogram Normal Curve Central Limit Theorem Outline 1 Todays G
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Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 16: More Box Models Tessa L. Childers-Day UC Berkeley 18 March 2014 Todays Goals EV and SE Normal Curve Classifying and Counting Outline 1 Todays Goals 2 EV and SE 3 Normal Curve 4 Classifying and Count
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Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 10: Errors in Regression Tessa L. Childers-Day UC Berkeley 18 February 2014 Todays Goals Why error? Estimation/Interpretation Residuals Strip Methods Outline 1 Todays Goals 2 Why error? 3 Estimation/Int
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Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 15: Law of Averages Tessa L. Childers-Day UC Berkeley 13 March 2014 Todays Goals Recap Law of Averages Box Models Outline 1 Todays Goals 2 Recap 3 Law of Averages 4 Box Models 2 / 21 Todays Goals Recap
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Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 8: Bivariate Data and Correlation Tessa L. Childers-Day UC Berkeley 13 February 2014 Todays Goals Summary Statistics Association Correlation Properties Outline 1 Todays Goals 2 Summary Statistics 3 Asso
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Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 14: Midterm Review Tessa L. Childers-Day UC Berkeley 6 March 2014 Midterm Guidelines Material Covered Q&A Details Tuesday, 11 March 2014 In lecture, this room Lasts 80 minutes (5:10pm to 6:30pm) Worth 2
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Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 13: Binomial Formula Tessa L. Childers-Day UC Berkeley 4 March 2014 Todays Goals Recap Counting Calculating Probabilities Examples Outline 1 Todays Goals 2 Recap 3 Counting 4 Calculating Probabilities 5
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Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 3: Types of Data and Displays Tessa L. Childers-Day UC Berkeley 28 January 2014 Todays Goals Kinds of Data Displaying Qualitative Data Outline 1 Todays Goals 2 Kinds of Data 3 Displaying Qualitative Dat
School: Berkeley
Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 11: Introduction to Probability Tessa L. Childers-Day UC Berkeley 25 February 2014 Todays Goals What is probability? Box Models Probability Rules Outline 1 Todays Goals 2 What is probability? 3 Box Mode
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Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 5: Summary Statistics Tessa L. Childers-Day UC Berkeley 4 February 2014 Todays Goals Shape Location Spread Outline 1 Todays Goals 2 Shape 3 Location 4 Spread 2 / 28 Todays Goals Shape Location Spread By
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Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 12: More Probability Tessa L. Childers-Day UC Berkeley 27 February 2014 Todays Goals Recap More Rules and Techniques Examples Outline 1 Todays Goals 2 Recap 3 More Rules and Techniques 4 Examples 2 / 23
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Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 6: Normal Curve/Approximation Tessa L. Childers-Day UC Berkeley 6 February 2014 Todays Goals Normal Curve Approx. Normal Data Finding Areas Finding Percentiles Outline 1 Todays Goals 2 Normal Curve 3 Ap
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Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 9: Regression Methods Tessa L. Childers-Day UC Berkeley 20 February 2014 Todays Goals The Intuition The Mechanics Some Caveats Simplication Outline 1 Todays Goals 2 The Intuition 3 The Mechanics 4 Some
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Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 7: Measurement Error Tessa L. Childers-Day UC Berkeley 11 February 2014 Todays Goals Repeated Measurements Outliers Errors Outline 1 Todays Goals 2 Repeated Measurements 3 Outliers 4 Errors 2 / 18 Today
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Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 4: Data Displays (cont.) Tessa L. Childers-Day UC Berkeley 30 January 2014 Todays Goals Recap Displaying Quantitative Data Outline 1 Todays Goals 2 Recap 3 Displaying Quantitative Data 2 / 19 Todays Goa
School: Berkeley
Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 1: Experimental and Observational Studies Tessa L. Childers-Day UC Berkeley 21 January 2014 Todays Goals Course Introduction Experiments and Observations Outline 1 Todays Goals 2 Course Introduction 3 E
School: Berkeley
Course: STATISTICS
Stat 20: Intro to Probability and Statistics Lecture 2: Surveys and Sampling Tessa L. Childers-Day UC Berkeley 23 January 2014 Todays Goals Survey Basics and Language Types of Surveys Examples Outline 1 Todays Goals 2 Survey Basics and Language 3 Types of
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Course: Concepts In Computing With Data
11/15/12 Bank customer account information Mul)pleTables Wheredoyouseeredundancy? Whatmightanen)tybe?(e.g.labtest) BANKBRANCH BANKBRANCH CUSTOMER Wheredoyouseeredundancy? Whatmightanen)tybe?(e.g.labtest) Wheredoyouseeredundancy? Whatmightanen)tybe?(
School: Berkeley
Course: Concepts In Computing With Data
10/18/12 Elec0onStudy TextData GeographicDatalongitudeandla0tudeof thecountycenter Popula0onDatafromthecensusforeach county Elec0onresultsfrom2008foreachcounty (scrapedfromaWebsite) Wanttomatch/mergetheinforma0onfrom thesethreedierentsource Whatproblem
School: Berkeley
Course: Concepts In Computing With Data
9/3/12 Whyisgraphicsinthiscourse? Graphics Goodgraphicstodayrequiresthecomputer Visualiza>onenterseverystepofthedata analysiscycle Datacleaningarethereanomalies? Explora>on Modelchecking Repor>ngresults Plotscanuncoverstructureindatathatcantbe dete
School: Berkeley
Course: Concepts In Computing With Data
10/11/12 UNIX Aside:MacOSisactuallybuiltontopoftheUNIXkernel, soeverythingwe lldohereyoucanalsodoonthelab computers. TogettoawindowwithaUNIXcommandline(calleda terminal),gotoApplica/ons>U/li/es>Terminal. Ifyou reonaWindowsmachine,thereareprogramsto emulat
School: Berkeley
Course: Concepts In Computing With Data
10/11/12 Representa.onofNumbers Representa.onofColors Colors:(rgb) (255,0,0) #FF0000 (255,255,0) #FFFF00 (100,149,237) #6495ED Representa.onofData HTMLtable,ExcelSpreadsheet,plain text #E41A1C99 1 10/11/12 ManyEyeshtml ManyEyestext ASCII&Unicode ManyEyesx
School: Berkeley
Course: Concepts In Computing With Data
9/25/12 More on Functions Environments and variable scope R has a special mechanism for allowing you to use the same name in different places in your code and have it refer to different objects. For example, you want to be able to create new variables in
School: Berkeley
Course: Concepts In Computing With Data
9/14/12 Dataframes,Lists,Matrices 2012SummerOlympics ANDtheApplyFamilyofFunc>ons HowdidwecreatetheHW assignment? WorldRecordintheMens1500meter Howhave the>mes changed? Howmuch fasterare todays runners? > url = http:/en.wikipedia.org/wiki/1500_metres_world
School: Berkeley
Course: Concepts In Computing With Data
9/20/12 Writing your own functions Function we will write today Convert a vector of measurements in inches into centimeters So far we have relied on the built-in functionality of R to carry out our analyses. In the next several lectures, we ll cover How
School: Berkeley
Course: Concepts In Computing With Data
9/3/12 tail(): shows last 6 values summary(): min, 1st quartile, median, mean, 3rd quartile, max Sta;s;ciansperspec;ve DataTypes, Vectors,andSubse9ng DataTypes Rhasanumberofbuiltindatatypes.Thethree mostbasictypesarenumeric,character,and logical. Youcan
School: Berkeley
Course: Concepts In Computing With Data
10/25/12 ReadingandWri0ngDataFiles UnstructuredvsStructured PlaintextData StateoftheUnionSpeeches WebLogEntries * State of the Union Address George Washington December 8, 1790 Fellow-Citizens of the Senate and House of Representatives: In meeting you
School: Berkeley
Course: Concepts In Computing With Data
11/12/12 ProgrammingLanguages wehaveseensofar Rusescontrolowtodescribea computa>on shellcommandscommandlineinterfaceto theopera>ngsystem regularexpressionsdescribesapaAernbut nothowtondit HTMLdescribeswhatshouldappearona Webpagebutnothowtorenderit Xp
School: Berkeley
Course: Concepts In Computing With Data
To get the text in an attribute, use xmlGetAttr(node, "currency") 11/1/12 XMLpackageinR Handyfunc;onsforparsingXML XML eXtensibleMarkupLanguage ToreadanXMLleintoR,usexmlParse readHTMLTable:readsanHTMLtableintoR xmlParse:readanXMLleintoR xmlValue:retr
School: Berkeley
Course: Concepts In Computing With Data
10/30/12 Tweets TextMining StormpushesPresiden:alRacefromspotlight Romneyholdsslim1pointleadamonglikely votersinCOrace DidPennsylvaniarunmisleadingvoterIDad? MiIRomneyisjustnotthatintoFederal DisasterRelief ModiedTweets StormpushesPresiden:alRacefroms
School: Berkeley
Course: STATISTICS
Stat 20 Quiz 1 February 10, 2014 Please write your name below and circle your section. Answer the questions in the space provided. There are questions on the back. This quiz covers material from Homeworks 1 a
School: Berkeley
Course: STAT 21
Quiz 1 Statistics 21 Spring 2010 Ibser 1. A large class takes a test, and the table shows their scores. For all parts of this problem, assume that the scores are continuous and that they are evenly distributed within each separate class interval. The maxi
School: Berkeley
Course: STAT 21
Quiz 1 Solutions Statistics 21 Spring 2010 Ibser Each part of every problem is worth 2 pts except 1a worth 3 and 1b worth 1. 1. (a) Interval Percent Height 10-50 20 0.5 50-70 28 1.4 70-80 20 2 80-90 22 2.2 90-100 10 1 Draw histogram with these axes: x axi
School: Berkeley
Course: STATISTICS
Stat20 Quiz2 February24,2014 Name:_Section:101, 102,103,104 105,106,107,108 SOLUTIONS?pointspossible Part1Forquestions12,showallworkandputaboxaroundyouranswer.Forquestion3,no workisrequired.UsetheprovidedNormalTableonthebackifneeded. 1. ForfreshmenatUCBer
School: Berkeley
Course: Statistics For Business Majors
Stat 21, Fall 2011, Murali-Stoyanov Quiz 2 (v1) Answer Key 1a) (70-79)/8.5 = -1.06 ~ -1.05. Area = 70.63% (85-79)/8.5 = 0.71 ~ 0.70. Area = 51.61% (70.63%/2) + (51.61%/2) = 61.12% 1b) 35th Percentile -> Area = 30% (82-79)/8.5 = 0.35. Area = 27.37% (30%/2)
School: Berkeley
Course: Probability
Stat 134: problems before the nal exam Michael Lugo May 6, 2011 Some problems recommended to do before the nal exam: 6.4.6, 6.4.9, 6.4.12, 6.4.21, 6.5.2, 6.5.4, 6.5.6, 6.5.8, 6.R.8(c), 6.R.13(b), 6.R.14, 6.R.18, 6.R.25 6.4.6 Let X1 and X2 be the numbers o
School: Berkeley
Course: Intro To Probability And Statistics
Statistics 20: Midterm Solutions Summer Session 2007 1. [20 points] Pressure and Boiling Points. (a) [5 points] What is the equation of the regression line for predicting P RES from T EMP ? Solution: Here the x variable is TEMP in Fahrenheit and the y var
School: Berkeley
Course: Intro To Probability And Statistics
Statistics 20: Summer Session 2007 Quiz n. 1 Friday July 6, 2007 Full Name (Please print): ID: Lab: YOU MUST SHOW WORK TO RECEIVE ANY CREDIT 1. The British government conducts regular surveys of household spending. The average weekly household spending on
School: Berkeley
Course: STAT 21
Quiz 2 Statistics 21 Spring 2010 Ibser 1.)Suppose we have two sets of data A and B. a) Compute the correlation of X and Y of set A. b) Is there any number that could be put in the blank in set B which would make the correlation between X and Y equal to ze
School: Berkeley
Course: STATISTICS
Stat 20 Quiz 3 March 10, 2014 Name:_Section:101,102,103,104 105,106,107,108 1.Astatisticsclassisunhappywithitsmidtermperformance.Theclassmanagestopersuadetheprofessortogiveallthe studentstheopportunitytotakearetest.Twoscoreswillbepositivelyandlinearlycorr
School: Berkeley
UGBA 103, Midterm Exam: March 05, 2012 Name: ID: Section: The answers on this midterm are entirely my own work. I neither gave nor received any aid while taking this midterm. _ Signature Please remember to write your name legibly on every page. The maximu
School: Berkeley
Course: Probability
Statistics 2 Problems from past nal exams 1. (5 points) The paragraph below is taken from an article in the San Francisco Chronicle of Tuesday, March 21, 1995. The person quoted in the article is Patrick Portway, executive director of the United States Di
School: Berkeley
STAT 20 - Fall 2011 - Practice Midterm 1 Most explanations require just a sentence or two. On calculations, show your work and work through to a numerical answers, upto at least 2 decimal places. 1. Below are the statistics of 3 lists of numbers. The aver
School: Berkeley
Course: Concepts Of Probability
Stat 134 Final (Fall 2002) A. Bandyopadhya This final is from Antars 2002 course. I typed the questions recreating his test, since I had only the solutions. Mike Leong Fa 02 Exam 1. True/False Questions a) If () 0 and , then (|) (). 1 b) If , ~ such that
School: Berkeley
Course: Concepts Of Probability
Stat 134 Practice Final (Fall 2002) A. Bandyopadhya 1. Suppose is a random variable with the following density: 1 () = , < < (1 + 2 ) a) Find the CDF of |. b) Find the density of 2 . 2. Let 1 2 be the times of 1 and 2 arrivals in a Poisson arrival proces
School: Berkeley
Course: Concepts Of Probability
Stat 134 Midterm (Spring 2014) A. Bandyopadhya Sp 14 Exam 1. A point (, ) is randomly selected from the following finite set of points on the plane cfw_(, )|1 . a) What are the marginal distributions of and ? Is the pair (, ) exchangeable? Explain your an
School: Berkeley
Course: STATISTICS
Statistics 20 Practice Final Exam #1 1. (a) Approximately how many students scored between 525 and 575 on the mathematical test? We are told that the empirical histogram for SATmath follows a normal curve, centered on the average score of 475 with a stand
School: Berkeley
Course: STATISTICS
Stat 134 Fall 2009 A. Adhikari Answers to midterm practice problems I have left the answers as numerical formulas. Occasionally I have included the decimal value in [ ], but you wont be doing that on the exam. 1. 1/ 52 13 . No, you dont square it. The rst
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Stat 150 Midterm 1 Spring 2015 Instructor: Allan Sly Name: SID: There are 4 questions worth a total of 48 points. Attempt all questions and show your working - solutions without explanation will not receive full credit. Answer the questions in the space p
School: Berkeley
Course: STATISTICS
Quiz 1 Version 1 Solutions. 1. (a) The height of the bar over the interval 10 - 20 is _1.6 % per yr_ (specify the units) (b) The 55th percentile of the distribution is at: _38.5 yrs_ (units and 1 decimal place) (c) Circle the interval which is more crowde
School: Berkeley
Course: STATISTICS
Stat 20 Section 206 and 207 Handout 12/1/14 1. Review pg 345 in your reader. 2. Given that X is a binomial distribution with parameters n number of trials and probability of success p, what is P(X=x)? What are the possible values of X? 3. What is the stor
School: Berkeley
Course: STATISTICS
Stat 20 Section 206 and 207 Handout 11/5/14 Distribution of a Die Minimum of a 6-sided Fair Die For one die roll: Let X=number that appears on the die roll. Find: probability of X greater than or equal to 1: probability of X greater than or equal to 2: pr
School: Berkeley
Course: STATISTICS
Stat 20 Fall 2014 Finals Review PDF and CDF Probability Density Function (PDF) Definition: In pdfs, the area under the graph represents probabilities. For a pdf, the total area under the graph is 1. Why? Continuous random variable X has PDF f(x) if = for
School: Berkeley
Course: STATISTICS
Stat 20 Section 206 and 207 Handout Textbook pg 541 #2 As part of a study on the selection of grand juries in Alameda county, the educational level of grand jurors was compared with the county distribution: Educational Level Elementary Secondary Some Coll
School: Berkeley
Course: Concepts Of Probability
Stat 134: exam solutions Michael Lugo November 4, 2011 1. [6 = 2 + 2 + 2] I have a coin which comes up heads with probability 1/3, and you have a coin which comes up heads with probability 1/4. We both ip our coins at the same time. We repeat this procedu
School: Berkeley
Course: Concepts Of Probability
Stat 134: exam solutions Michael Lugo September 28, 2011 1. [1] Consider the following events: (i) in ipping 12 fair coins, exactly 6 heads are obtained. (ii) in ipping 108 fair coins, either 53, 54, or 55 heads are obtained. Which of the following statem
School: Berkeley
Course: Concepts Of Probability
Stat 134: nal exam solutions Michael Lugo December 16, 2011 1. [8: 2 + 2 + 2 + 2] Let H be the number of heads in 150 tosses of a biased coin with probability 0.4 of coming up heads. Find normal approximations to: (a) P (56 H 64) (b) P (59 H 67) (c) P (H
School: Berkeley
Course: Concepts Of Probability
University of California, Berkeley, Statistics 134: Concepts of Probability Michael Lugo, Fall 2011 Exam 1 September 28, 2011, 12:10 pm - 1:00 pm Name: Student ID: This exam consists of eight pages: this cover page; six pages containing problems; and a ta
School: Berkeley
Course: Concepts Of Probability
University of California, Berkeley, Statistics 134: Concepts of Probability Michael Lugo, Fall 2011 Final exam December 16, 2011, 11:40 am - 2:30 pm Name: Student ID: This exam consists of fourteen pages: this cover page, ten pages each containing one pro
School: Berkeley
Course: Concepts Of Probability
University of California, Berkeley, Statistics 134: Concepts of Probability Michael Lugo, Spring 2011 Final exam May 10, 2011, 7:10 - 10:00 pm Name: Student ID: This exam consists of twelve pages: this cover page; ten pages containg problems; and a table
School: Berkeley
Course: Concepts Of Probability
University of California, Berkeley, Statistics 134: Concepts of Probability Michael Lugo, Spring 2011 Exam 2 solutions 1. A fair twenty-sided die has its faces labeled 1, 2, 3, . . . , 20. The die is rolled sixteen times. Find: (a) [5] The expected value
School: Berkeley
Course: Concepts Of Probability
University of California, Berkeley, Statistics 134: Concepts of Probability Michael Lugo, Fall 2011 Exam 2 November 4, 2011, 12:10 pm - 1:00 pm Name: Student ID: This exam consists of seven pages: this cover page; ve pages containing problems; and a table
School: Berkeley
Course: Concepts Of Probability
University of California, Berkeley, Statistics 134: Concepts of Probability Michael Lugo, Spring 2011 Exam 2 April 6, 2011, 11:10 am - 12:00 noon Name: Student ID: This exam consists of seven pages: this cover page; ve pages containg problems; and a table
School: Berkeley
Course: Concepts Of Probability
University of California, Berkeley, Statistics 134: Concepts of Probability Michael Lugo, Spring 2011 Final exam May 10, 2011, 7:10 10:00 pm Name: (Decemb(ri 1/ Student ID: 3 1 5' 6 This exam consists of twelve pages: this cover page; ten pages containg
School: Berkeley
Course: Introductory Probability And Statistics For Busines...
QUIZ 5 - THE LAST QUIZ! HOORAY! 1. (2 points each) True/False. For each part below, answer true or false, and explain your answers briey (1-2 sentences). (a) The test statistic measures the dierence between the observed result and the result expected unde
School: Berkeley
Course: Introductory Probability And Statistics For Busines...
STAT 20 QUIZ 4 - STUDENT SOLUTIONS 1. You are ipping a biased coin that lands heads 75% of the time. You have the option of ipping 100 times or 10,000 times. State which option is better and explain briey, if you win when. a. .you get at least 70% heads?
School: Berkeley
Course: Introductory Probability And Statistics For Busines...
STAT 20 QUIZ 3 - SOLUTIONS 1. The following information was collected from a survey of sports fans viewing habits. 28% 29% 14% 73% watch baseball watch basketball watch both baseball and basketball dont watch either baseball or basketball a. Find the prob
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Stat 150 Practice Midterm Spring 2015 Instructor: Allan Sly Name: SID: There are 4 questions worth a total of 61 points plus 4 bonus points. Attempt all questions and show your working - solutions without explanation will not receive full credit. Answer t
School: Berkeley
Course: Concepts In Computing With Data
STAT 133 Practice Midterm Questions 1. What makes a data frame dierent from a list? 2. Name three characteristics of R that make it particularly suited to statistical analysis. 3. Rewrite the following code to make it vectorized: x = numeric(30) for (i in
School: Berkeley
Course: Concepts Of Statistics
Name: Student ID Number: Statistics 135 Fall 2007 Midterm Exam Ignore the nite population correction in all relevant problems. The exam is closed book, but some possibly useful facts about probability distributions are listed on the last page. Show your w
School: Berkeley
Course: Concepts Of Probability
Stat 134 Midterm Instructor: Mike Leong Name: Summer 2012 _ To get credit for work, you must show your work. Box in your final answer. # Your Score Points Possible 1 15 2 10 3 10 4 5 5 10 Total 50 Stat 134 Stat 134 Midterm Page 1 of 6 1. A building has 10
School: Berkeley
Course: Concepts Of Probability
Stat 134 Midterm Instructor: Mike Leong Name: Summer 2013 _ To get credit for work, you must show your work. Box in your final answer. This test will be scanned. Please write all your work on the right pages and write your name on each page. # Your Score
School: Berkeley
Course: Concepts Of Probability
Stat 134 Midterm Solution, Summer 2013 1. Suppose X ~ Pois ( ) . a) Here is an algebra problem. Simplify x 3x( x 1) x( x 1)( x 2) . x 3x( x 1) x( x 1)( x 2) x (3x 3x) ( x 3x 2 x) x 2 3 2 (2 pts) 3 b) Find E ( X 3 ) . (4 pts) E (X ) E[( X ) 2 ] x( x 1)e
School: Berkeley
Course: Concepts Of Probability
Review Problems for Final Chapter 4 1. Alix and Nikita, while waiting at a bus terminal, got into an argument and decided to split up as a spy team. Nikita wants to take bus line B. Alix can take either bus line A or bus line B, but she doesnt want to be
School: Berkeley
Course: Concepts Of Probability
Midterm Format There are 5 questions on the midterm. Most questions will have multiple parts. The beginning parts tend to be easier, so you may to skip around and come back to questions that are more difficult after you have tried to do all the easier one
School: Berkeley
Course: Concepts Of Probability
M362K (56310), Sample Midterm 1 Instructions: Please show all your work, not only your nal answer, in order to receive credit. Please keep answers organized in the same order the problems have been assigned. Recommended time: 1 hour 1. (Pitman, p. 490, #1
School: Berkeley
Course: Concepts Of Probability
Stat 134 Study Group Fac: Professor Pitman SGL: Mike Leong, mleong@berkeley.edu Loc: 11-12 pm, 310 Hearst Mining Circle Community through Academics and Leadership Chapter 3: Random Variables Chapter 3 Table of Contents Chapter 3: Random Variables . 1 Chap
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Course: Concepts Of Probability
Chapter 1: Introduction Chapter 1 Table of Contents Chapter 1: Introduction . 1 Chapter 1 Table of Contents . 1 Chapter 1 Worksheets . 1 1.1 Worksheet: Equally Likely Outcomes . 2 1.2 Worksheet: Interpretations . 4 1.3 Worksheet: Distributions . 6 1.4 Wor
School: Berkeley
Course: Concepts Of Probability
Stat 134 MIDTERM (Fall 2012) J. Pitman. Name and SID number: This is an open book exam. Please circle nal answers. Show your work in space provided. 1. Let Sn,p denote a random variable with the binomial distribution with parameters n and p. Find xn,p suc
School: Berkeley
Course: Theoretical Statistics
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 5 - Solutions Fall 2008 Issued: Tuesday, September 29, 2009 Problem 5.1 First, notice that we can rewrite: p(x; ) = exp [x log log ( log(1 )] so p belongs
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STAT516 Solution to Homework 2 1.4.5: a) Let U1=(urn 1 chosen), U2=(urn 2 chosen), B=(black ball chosen), W=(White ball chosen). 2/5 B 1/2 U1 3/5 4/7 W B 1/2 U2 3/7 W b) P(U1)=1/2=P(U2); P(W|U1)=3/5; P(B|U1)=2/5; P(W|U2)=3/7; P(B|U2)=4/7 c) P(B)=P(B|U1)P(
School: Berkeley
UC Berkeley Department of Electrical Engineering and Computer Science Department of Statistics EECS 281A / STAT 241A Statistical Learning Theory Solutions to Problem Set 3 Fall 2011 Issued: Monday, October 10, 2011 Due: Monday, October 24, 2011 Reading: F
School: Berkeley
Course: Probability
Homework 10 Solutions 5.2.4 Statistics 134, Pitman , Fall 2012 a) y x 6e2x3y dydx P (X x, Y y ) = 0 0 x = 0 y 1 6e2x ( e3y ) dx 3 0 x 2e2x dx = (1 e3y ) 0 3y = (1 e b) )(1 e2x ) 6e2x3y dy = 2e2x fX (x) = 0 c) 6e2x3y dx = 3e3y fY (y ) = 0 d) Yes, they are
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Math 361/Stat 351 X1 Homework 10 Solutions Spring 2003 Graded problems: 1(d), 3(c), 4(b), 7 Problem 1. [4.2.4] Suppose component lifetimes are exponentially distributed with mean 10 hours. Find (a) the probability that a component survives 20 hou
School: Berkeley
Course: Theoretical Statistics
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 1 Fall 2007 Issued: Thursday, August 30 d p m.s. Due: Thursday, September 6 Notation: The symbols cfw_, , denote convergence in distribution, probability
School: Berkeley
Course: 135
Stat 135, Fall 2011 HOMEWORK 8 due WEDNESDAY 11/9 at the beginning of lecture Friday 11/11 is a holiday, so this is a very short homework due two days earlier at the start of lecture. Grading: A (4 points) for all three problems done well, B (2 points) fo
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Statistics 20: Quiz 4 Solutions 1. A team of doctors want to estimate the life expectancy of students afflicted with the rare genetic disease statinotisticitis; however, only 15 known cases have ever been diagnosed. The sample reported a mean lifespa
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Statistics 20: Quiz 1 Solutions Speed (mph) 0-10 10-20 20-40 40-80 80-95 Percentage of Total Cars 20 10 40 20 10 The above table depicts data collected in a (hypothetical) survey studying the distribution of traffic speed on the Bay Bridge. Each gro
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UC Berkeley Department of Electrical Engineering and Computer Science Department of Statistics EECS 281A / STAT 241A Statistical Learning Theory Problem Set 5 Fall 2011 Issued: Thursday, November 10, 2011 Due: Wednesday, November 30, 2011 Problem 5.1 Conv
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Course: 135
Stat 135, Fall 2011 A. Adhikari HOMEWORK 4 (due Friday 9/30) 1. 8.20. Use R to do this one accurately. Be careful about constants when youre working out the distribution of 2 . 2. 8.32. You dont have to do all six intervals in parts (b) and (c); just do t
School: Berkeley
Course: 135
Stat 135, Fall 2011 A. Adhikari HOMEWORK 5 (due Friday 10/7) 1. 9.11. Use R to do the plots accurately. In each case, say what the limiting power is as approaches 0. 2. 9.12. 3. 9.13. In c, use R to nd the critical values x0 and x1 . Turn the page for d.
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UC Berkeley Department of Electrical Engineering and Computer Science Department of Statistics EECS 281A / STAT 241A Statistical Learning Theory Problem Set 3 Fall 2011 Issued: Monday, October 10, 2011 Due: Monday, October 24, 2011 Reading: For this probl
School: Berkeley
Course: Theoretical Statistics
UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 8 Fall 2006 Issued: Thursday, October 26, 2006 Due: Thursday, November 2, 2006 Some useful notation: The pth quantile of a continuous random variable with
School: Berkeley
Course: Probability
Homework # 2 Statistics 134, Pitman , Spring 2009 2.1.2 P (2 boys and 2 girls) = 4 (1/2)4 = 6/24 = 0.375 < 0.5. So families with dierent 2 numbers of boys and girls are more likely than those having an equal number of boys and girls, and the relative freq
School: Berkeley
School: Berkeley
Course: Introductory Probability And Statistics For Busines
- Home | Text Table of Contents | Assignments | Calculator | Tools | Review | Glossary | Bibliography | System Requirements | Author's Homepage Chapter 21 Testing Equality of Two Percentages Chapter 19, "Hypothesis Testing: Does Chance Explain the Results
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UC Berkeley Department of Electrical Engineering and Computer Science Department of Statistics EECS 281A / STAT 241A Statistical Learning Theory Problem Set 1 Fall 2011 Issued: Thurs, September 8, 2011 Due: Monday, September 19, 2011 Reading: For this pro
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UC Berkeley Department of Electrical Engineering and Computer Science Department of Statistics EECS 281A / STAT 241A Statistical Learning Theory Solutions to Problem Set 1 Fall 2011 Issued: Thurs, September 8, 2011 Due: Monday, September 19, 2011 Reading:
School: Berkeley
Course: 135
Stat 135, Fall 2011 HOMEWORK 1 (due Friday 9/9) 1a) Let x1 , x2 , . . . , xn be a list of numbers with mean and SD . Show that 2 = 1 n n x2 2 i i=1 b) A class has two sections. Students in Section 1 have an average score of 75 with an SD of 8. Students in
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Math 361 X1 Homework 4 Solutions Spring 2003 Graded problems: 1(b)(d); 3; 5; 6(a); As usual, you have to solve the problems rigorously, using the methods introduced in class. An answer alone does not count. The problems in this assignment are inte
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Math 361 X1 Homework 6 Solutions Spring 2003 Graded problems: 2(a);4(a)(b);5(b);6(iii); each worth 3 pts., maximal score is 12 pts. Problem 1. [3.1:4] Let X1 and X2 be the numbers obtained on two rolls of a fair die. Let Y1 = max(X1 , X2 ) and Y2
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Math 361 X1 Homework 9 Solutions Spring 2003 Graded problems: 1(a), 2, 4(b), 5(b) (3 points each - 12 points maximal); 7 (Bonus problem): up to 2 additional points Problem 1. [4.R:25, variant] Suppose U is distributed uniformly on the interval (0
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Math 361 X1 Homework 8 Solutions Spring 2003 Graded problems: 1, 4(b), 5, 6; 3 points each, 12 points total Problem 1. In a certain math class each homework problem is scored on a 0 3 point scale. A lazy grader decides to grade these problems by
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Math 361 X1 Homework 1 Solutions Spring 2003 Graded problems: 1; 2(b);3;5; each worth 3 pts., maximal score is 12 pts. Problem 1. A coin is tossed repeatedly. What is the probability that the second head appears at the 5th toss? (Hint: Since only
School: Berkeley
Course: Concepts Of Probability
Homework # 12 Statistics 134, Bandyopadhyay, Spring 2014 4.2.6 A Geiger counter is recording background radiation at an average rate of one hit per minute. Let T3 be the time in minutes when the third hit occurs after the counter is switched on. Find P (2
School: Berkeley
Course: Concepts Of Probability
Homework # 1 1.1.3 Statistics 134, Bandyopadhyay, Spring 2014 a) If the tickets are drawn with replacement, then, as in Example 1, there are n2 equally likely outcomes. There is just one pair in which the rst number is 1 and the second number is 2, so P (
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Stat 150 Homework # 5 Solutions 1: Recall that Zn /n is a martingale. In particular, by the conservation of expectation property of martingales, E[Zn ] = n . The total number of individuals in all the generations combined is simply n0 Zn . Consequently, E
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Stat 150 Homework # 7 Solutions A summary of some useful facts: A continuous-time Markov chain (Yt )tR+ on a finite state space can be described in several ways: (i) By its generator G. In which case Ht (x, y) := Pr[Yt = y | Y0 = x] = (etQ )x,y . In which
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Stat 150 Homework # 4 Solutions 1: Let X Geometric(p). Then p[(1 p)s]k = GX (s) = k=0 p , 1 (1 p)s Let Y1 , Y2 , . . . be i.i.d. Bernoulli(q) random variables, such that X, Y1 , Y2 , . . . , are independent. Dene Y := X Yi . Then Y Bin(X, q). We have that
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Stat 150 Homework # 9 Solutions 1: By the stationarity of BM this is like 2 + W1 given that W2 = 2. 1 First way - using scaling: Bt = 2 W2t is a standard BM if Wt is. So what we have is like = 2 + 2B1/2 given that B1 = 2. You saw in lecture that given tha
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Stat 150 Homework # 6 Solutions 1: Denote t0 = 0 = x0 , si := ti ti1 and yi = xi xi1 . Then 3 cfw_N (ti ) = xi = i=1 3 i=1 cfw_N ([ti ti1 ) = yi (up to an event of 0 probability in which there was an arrival in one of the times cfw_t1 , t2 , t3 . Thus b
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Stat 150 Homework # 8 Solutions 1: If the density function of a distribution has the form ck, xk1 ex , then ck, must be the normalizing constant xk11 x dx and immediately from the functional form of the density e (i.e. being some constant times xk1 ex ) w
School: Berkeley
Course: STATISTICS
Normal Approximation for Probability Histogram Chapter 18, Freedman, Pisani and Purves Review Exercises Problem 1. (Enhanced; most major points in the chapter covered in this problem) What is the chance that when you roll 8 dice, the sum will be from 20 t
School: Berkeley
Course: STATISTICS
Review Problems Chapter 23 - Accuracy of Averages Main point: The formulas for a percentage and an average are similar. A percentage is an average for a box model composed of zeros and ones, an average can be based on any arbitrary box model (incomes of f
School: Berkeley
Course: STATISTICS
Review Exercises Chapter 21 - The Accuracy of Percentages Central ideas: Statistical inference (sample -> box -> sample error); bootstrapping; confidence interval). See Exercise set A (7,8,9) and set C (4,5,6) for good exercises to master the language. Co
School: Berkeley
Course: STATISTICS
Review Exercises Chapter 20 - Chance Errors in Sampling 1. Tossing a fair coin: Find EV and SE for sums and percentages as the tosses increase from 100 to 2500 to 10,000 to 1,000,000 Box model will be [ 0 1 ] for a fair coin, so mean = 0.5 and SD = 0.5 To
School: Berkeley
Course: STATISTICS
Statistics Review Problems - Stat 1040 - Dr. McGahagan Chapter 17 - The Expected Value and the Standard Error (pp. 304-306) * 1.One hundred draws with replacement from the box [ 1 6 7 9 9 10 ]. Find the sum. a. May be as small as 100 (all ones) or as larg
School: Berkeley
Course: STATISTICS
Statistics Review Problems - Stat 1040 - Dr. McGahagan Chapter 16 (pp. 285-86 of 3rd edition) - The Law of Averages Be sure to review 1-8 carefully. 1. Box with 400 zeros and 600 ones. 1000 draws with replacement. Which best describes the situation? a. Ex
School: Berkeley
Course: STATISTICS
Statistics 1040 Review Exercises - Chapter 15 Binomial Formula Problem 1. Roll a die 6 times. Probability of exactly one ace = ? On any one throw, P (Ace) = 1/6 and P (Non-Ace) = 5/6. We can get EXACTLY one ace if we get: a. ace on first throw AND non-ace
School: Berkeley
Course: STATISTICS
Statistics 1040 Review Exercises - Chapter 14 More About Chance Problem 1. Calculate the odds - pair of dice a. Chance both show 3 = chance first shows 3 AND second shows 3 = multiplication rule, each die is independent, so simple multiplication rule appl
School: Berkeley
Course: STATISTICS
Review Questions - Chapter 12 - The Regression Line Statistics 1040 - Dr. McGahagan * Problem 1. Find the regression equation - E [Final | Midterm] = a + b * Midterm Average score on midterm = 70; SD on midterm = 10 Average score on final = 55; SD on fina
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Course: STATISTICS
Review Questions - Chapter 10 - Regression Statistics 1040- Dr. McGahagan Problem 1. Scatter diagrams. Requires graph from textbook; match the description with the graph. (i) Total score below 1000 - Graph A - shaded under the diagonal line from (200, 800
School: Berkeley
Course: STATISTICS
Review Exercises Normal Approximation to Data Chapter 5, FPP, p. 93-96 Dr. McGahagan Problem 1. Test scores and the normal approximation. Given: Mean = 50, SD = 10 A 1.25 SD interval around the mean = 50 +/- 12.5 = 37.5 to 62.5 Using the normal tables fro
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Course: STATISTICS
Review Questions - Chapter 11 - RMS Error Statistics 1040 - Dr. McGahagan Problem 1. Formula for RMS error. RMS error = (sqrt (1 - R-squared) * SDy Problem 2. Expected value of GPA in college given GPA in high school The program with a RMSE of 3.12 is not
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Course: STATISTICS
Review Exercises Average and Standard Deviation Chapter 4, FPP, p. 74-76 Dr. McGahagan Problem 1. Basic calculations. Find the mean, median, and SD of the list x = (50 41 48 54 57 50) Mean = (sum x) / 6 = 300 / 6 = 50 Median = 50. Note that the list must
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Course: STATISTICS
Chapter 3 - Review Exercises Statistics 1040 - Dr. McGahagan Problem 1. Histogram of male heights. Shaded area shows percentage of men between 66 and 72 inches in height; this translates as "66 inches OR more, AND less than 72 inches." Note that since the
School: Berkeley
Course: STATISTICS
Chapter 9 - Exercise Sets A and B. Statistics 1040 - Dr. McGahagan In the chapter: Exercise sets A and B make one point which is worth taking a bit of extra time over: Problem 2. Corr (x, y) = Corr (y, x) X = (1 2 3 4 5) and Y = ( 2 3 1 5 6) Plot the poin
School: Berkeley
Course: STATISTICS
Review Exercises Chapter 6 - Measurement Error Pages 104-108 REVIEW EXERCISES (page 104) Problem 1. Do you only need to measure once? Answer: NO, no matter how experienced you are. You will NOT get the same result both times: try it yourself - measure the
School: Berkeley
Course: STATISTICS
Chapter 8 - Review Exercises Statistics 1040 - Dr. McGahagan Correlation Simple warmup exercises: Do these by hand, and check your computation on a computer. Have the computer draw the plots: (plot y x), (plot z x) and so on. Begin with: (bind x (list 1 2
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Stat 150 - Section 3 - Reversible Markov Chains Irreducibility: For all x, y, there exists some k > 0 s.t. P k (x, y) > 0 (think about this property as connectivity). A chain has period k if for all x we have that pn (x, x) > 0 implies that n is divisib
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Stat 150 - Section 2 - Martnigales and Optional Stopping Recall: We say that a sequence of r.v.s (Mn ) is a martingale w.r.t. (Yn ) if Mn n=0 n=0 is determined by (Y0 , . . . , Yn ) for all n and E[Mn+1 | Y0 , Y1 , . . . , Yn ] = Mn , for all n 0. (1) U
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Stat 150 Homework # 3 Due February 20 Problems: Q 1 On a game show there are two contestants. A contestant answers a series of questions until they make a mistake and then it becomes the other contestants turn. Contestant one answers questions correctly 7
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Stat 150 Homework # 4 Due May 6 Problems: Q 1 Let X be a geometric random variable with success probability p (i.e. P[X = k] = (1 p)k p for k = 0, 1, . . .). Find the probability generating function for X (see Mondays class). Let Y have distribution Bin(X
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Stat 150 Homework # 5 Due May 13 Problems: Q 1 Let Zn be a branching process with ospring distribution X. Suppose that X has mean < 1. Calculate the total expected number of ospring in all the generations. Q 2 Let Zn be a branching process with ospring d
School: Berkeley
Course: Concepts Of Probability
HW 12: 4.R (16, 18, 21, 22) 6.1 (6, 7, 8, 9) 4.R 16 Let Ti = time of the ith car arrival at a toll booth. Suppose Ti ~ PAP ( 3) . a) Find P(T3 T1 3) . (t )0 (t )1 P(T3 T1 t ) P(T2 t ) 1 P(T2 t ) 1 e ( t ) 1! 0! (9)1 9 P(T3 T1 3) 1 e 9 1 1 10e 1!
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Course: Concepts Of Probability
HW 9: 4.4 (5, 6, 8, 10) 4.5 (4, 5, 7, 9) 4.4 5 Let X ~ Unif (1,2) and Y X 2 . Find fY (y) . Method 1: Change of Variable dx 1 X Y dy 2 y fY ( y ) f X ( x ) x: y x 2 1 1 1 1 0 y 1 1 2 y 0 y 1 dx 3 2 y 2 y 3 1 dy 1 1 1 y2 1 y 4 1 y 4 3 2 y 6 Met
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Course: Concepts Of Probability
HW 8: 4.1 (4, 6, 12) 4.2 (2, 4, 6, 8, 9) 4.1 4 Suppose X has density f X ( x) cx 2 (1 x)2 for 0 x 1 , and f X ( x) 0 otherwise. Find: a) the value of c Method 1: Integration 1 1 1 3 1 4 1 51 1 1 1 2 2 2 3 4 1 cx (1 x) dx c ( x 2 x x )dx c x x x c 3 2 5
School: Berkeley
Course: Concepts Of Probability
HW 14: 6.4 (4, 8, 10, 21, 22) 6.5 (2, 6, 12) 6.4 4 Suppose (X, Y) is uniformly distributed over the 4 points: (-1,0), (0,1), (0, -1), (1,0). Show X and Y are uncorrelated, but not independent. 0 1 0.25 0.25 0 0 0 0 0 -1 0.25 0.25 y -1 0 1 x Show X and Y
School: Berkeley
Course: Concepts Of Probability
HW 13: 6.2 (2, 4, 6, 11) 6.3 (2, 8, 10, 12) 6.2 2 Suppose U1,U 2 ~ iid Unif (1, n) . Let X min(U1,U 2 ) and Y max( U1 ,U 2 ) . Find: a) E (Y | X x) Method 1: Conditional Probability n E (Y | X x) yP (Y y | X x) xP (Y x | X x) yx x n yP(Y y | X x) y x
School: Berkeley
Course: Concepts Of Statistics
STAT 135 Lab 7 Distributions derived from the normal distribution, and comparing independent samples. March 16, 2015 The 2 distribution The 2 distribution We have seen several instances of test statistics which follow a 2 distribution, for example, the ge
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Course: Concepts Of Statistics
Lab 7 solutions STAT 135 Fall 2015 March 16, 2015 Exercise 1: Moment generating functions For each of the following distributions, calculate the moment generating function, and the rst two moments. 1. X P oisson() Recall that the moment generating functio
School: Berkeley
Course: Concepts Of Statistics
Lab 6 solutions STAT 135 Fall 2015 March 8, 2015 Exercise 1: Hypothesis testing and CI Duality Suppose that X1 = x1 , ., Xn = x1 , are such that Xi N (, and known. Show that the hypothesis test which tests 2 ) with unknown H0 : = 0 H1 : 6= 0 at signicance
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Course: Concepts Of Statistics
STAT 135 Lab 6 Hypothesis Testing March 8, 2015 The duality between CI and hypothesis testing The duality between CI and hypothesis testing Recall that the acceptance region was the range of values of our test statistic for which H0 will not be rejected a
School: Berkeley
Course: Concepts Of Statistics
Exercise 1: Bootstrapping Suppose that a sample consists of the following observations: 78, 86, 97, 91, 83, 89, 92, 88, 79, 68 Then the -trimmed mean is the average of the inner (1 2) values in the sample. For example, if = 0.2, then the trimmed mean is t
School: Berkeley
Course: Concepts Of Statistics
STAT 135 Lab 5 Bootstrapping and Hypothesis Testing March 2, 2015 The Bootstrap Bootstrap Suppose that we are interested in estimating a parameter from some population with members x1 , ., xM , but that this population is so large that we cannot possibly
School: Berkeley
Course: Concepts Of Statistics
Quick Announcement: Write your submission ID for the class on the top-left side of all future homeworks (including homework 4) You can check your submission ID in the HW 3 Grade comment section on BCourses. (This will help us signicantly in sorting future
School: Berkeley
Course: Concepts Of Statistics
STAT 135 Lab 4 solutions February 23, 2015 Exercise 1: Exercise 2: Su ciency (Problem 21 of Section 8.10 of Rice) Suppose that X1 , ., Xn are i.i.d with density function f (x|) = e (x ) , x and f (x|) = 0 otherwise. 1. Find the method of moments estimate
School: Berkeley
Course: Concepts Of Statistics
STAT 135 Lab 3 solutions February 9, 2015 Exercise 1: MLE: Asymptotic results In class, you showed that if we have a sample Xi P oisson(0 ), the MLE of is 1 M L = X n = n n Xi i=1 1. What is the asymptotic distribution of M L (You will need to calculate t
School: Berkeley
Course: Concepts Of Statistics
STAT 135 Lab 3 Asymptotic MLE and the Method of Moments February 9, 2015 Maximum likelihood estimation (a reminder) Maximum likelihood estimation Suppose that we have a sample, X1 , X2 , ., Xn , where the Xi are IID. Then the Maximum likelihood estimator
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Course: Concepts Of Statistics
STAT 135 Lab 2 Condence Intervals, MLE and the Delta Method February 2, 2015 Condence Intervals Condence intervals What is a condence interval? A condence interval is calculated in such a way that the interval contains the true value of with some specied
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Course: Concepts Of Statistics
STAT 135 Lab 2 solutions February 2, 2015 Exercise 1: condence intervals (a) In R, generate 1000 random samples, x1 , x2 , ., x1000 , from a (continuous) Uniform(5, 15) distribution We can simply use the runif() function # load in libraries I'm going to u
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Course: Concepts Of Statistics
STAT 135 Lab 1 Solutions January 26, 2015 Introduction To complete this lab, you will need to have access to R and RStudio. If you have not already done so, you can download R from http:/cran.cnr.berkeley.edu/, and RStudio from http:/www.rstudio.com/. You
School: Berkeley
Course: Concepts Of Statistics
STAT 135 Lab 1 January 26, 2015 Introduction To complete this lab, you will need to have access to R and RStudio. If you have not already done so, you can download R from http:/cran.cnr.berkeley.edu/, and RStudio from http:/www.rstudio.com/. You will have
School: Berkeley
Stat 215B (Spring 2005): Lab 3 GSI: Victor Panaretos victor@stat.berkeley.edu Due March 8 at the Lab Section Part 1 : Simultaneous Inference In this section we revisit the data from the previous lab. Recall that the scenario involved the study of li
School: Berkeley
Course: Statistical Genomics
We conclude that Y1 and Y2 have covariance 2 2 Cov [Y1 , Y2 ] = CY (1, 2) = (1 2 ) sin cos . (4) Since Y1 and Y2 are jointly Gaussian, they are independent if and only if Cov[Y1 , Y2 ] = 0. 2 2 Thus, Y1 and Y2 are independent for all if and only if 1 = 2
School: Berkeley
Course: Statistical Genomics
(c) Y has correlation matrix RY = CY + Y Y = 1 43 55 8 + 0 9 55 103 8 0 = 1 619 55 9 55 103 (6) (d) From Y , we see that E[Y2 ] = 0. From the covariance matrix CY , we learn that Y2 has 2 variance 2 = CY (2, 2) = 103/9. Since Y2 is a Gaussian random varia
School: Berkeley
Course: Statistical Genomics
Problem 5.3.7 Solution (a) Note that Z is the number of three page faxes. In principle, we can sum the joint PMF PX,Y,Z (x, y, z) over all x, y to nd PZ (z). However, it is better to realize that each fax has 3 pages with probability 1/6, independent of a
School: Berkeley
Course: Statistical Genomics
Problem 5.5.2 Solution The random variable Jn is the number of times that message n is transmitted. Since each transmission is a success with probability p, independent of any other transmission, the number of transmissions of message n is independent of
School: Berkeley
Course: Statistical Genomics
Problem 5.6.4 Solution Inspection of the vector PDF f X (x) will show that X 1 , X 2 , X 3 , and X 4 are iid uniform (0, 1) random variables. That is, (1) f X (x) = f X 1 (x1 ) f X 2 (x2 ) f X 3 (x3 ) f X 4 (x4 ) where each X i has the uniform (0, 1) PDF
School: Berkeley
Course: Statistical Genomics
Problem 5.6.9 Solution Given an arbitrary random vector X, we can dene Y = X X so that CX = E (X X )(X X ) = E YY = RY . (1) It follows that the covariance matrix CX is positive semi-denite if and only if the correlation matrix RY is positive semi-denite.
School: Berkeley
Course: Statistical Genomics
Problem Solutions Chapter 5 Problem 5.1.1 Solution The repair of each laptop can be viewed as an independent trial with four possible outcomes corresponding to the four types of needed repairs. (a) Since the four types of repairs are mutually exclusive ch
School: Berkeley
Course: Statistical Genomics
Frequency 150 100 50 0 1.7076 1.7078 1.708 1.7082 1.7084 1.7086 1.7088 1.709 1.7092 1.7094 1.7096 7 J x 10 If you go back and solve Problem 5.5.5, you will see that the jackpot J has expected value E[J ] = (3/2)7 106 = 1.70859 107 dollars. Thus it is not
School: Berkeley
Course: Statistical Genomics
Problem 5.4.2 Solution The random variables N1 , N2 , N3 and N4 are dependent. To see this we observe that PNi (4) = pi4 . However, 4 4 4 4 PN1 ,N2 ,N3 ,N4 (4, 4, 4, 4) = 0 = p1 p2 p3 p4 = PN1 (4) PN2 (4) PN3 (4) PN4 (4) . (1) Problem 5.4.3 Solution We wi
School: Berkeley
Course: Statistical Genomics
The off-diagonal zero blocks are a consequence of Y1 Y2 being independent of Y3 Y4 . Along the diagonal, the two identical sub-blocks occur because fY1 ,Y2 (x, y) = f Y3 ,Y4 (x, y). In short, the matrix structure is the result of Y1 Y2 and Y3 Y4 being iid
School: Berkeley
Course: Statistical Genomics
Problem Solutions Chapter 6 Problem 6.1.1 Solution The random variable X 33 is a Bernoulli random variable that indicates the result of ip 33. The PMF of X 33 is 1 p x =0 p x =1 PX 33 (x) = (1) 0 otherwise Note that each X i has expected value E[X ] = p
School: Berkeley
Course: Statistical Genomics
This implies 1 E [Y1 ] = E [Y3 ] = 2y(1 y) dy = 1/3 (3) 2y 2 dy = 2/3 (4) 0 1 E [Y2 ] = E [Y4 ] = 0 Thus Y has expected value E[Y] = 1/3 2/3 1/3 2/3 . The second part of the problem is to nd the correlation matrix RY . In fact, we need to nd RY (i, j) = E
School: Berkeley
Course: Statistical Genomics
Finally, the probability that more laptops require motherboard repairs than keyboard repairs is P [N2 > N3 ] = PN2 ,N3 (1, 0) + PN2 ,N3 (2, 0) + PN2 ,N3 (2, 1) + PN2 (3) + PN2 (4) (10) where we use the fact that if N2 = 3 or N2 = 4, then we must have N2 >
School: Berkeley
Course: Statistical Genomics
function p=sailboats(w,m) %Usage: p=sailboats(f,m) %In Problem 5.8.4, W is the %winning time in a 10 boat race. %We use m trials to estimate %P[W<=w] CX=(5*eye(10)+(20*ones(10,10); mu=35*ones(10,1); X=gaussvector(mu,CX,m); W=min(X); p=sum(W<=w)/m; > sailb
School: Berkeley
Course: Statistical Genomics
Problem 5.4.7 Solution Since U1 , . . . , Un are iid uniform (0, 1) random variables, 1/T n 0 u i 1; i = 1, 2, . . . , n 0 otherwise fU1 ,.,Un (u 1 , . . . , u n ) = (1) Since U1 , . . . , Un are continuous, P[Ui = U j ] = 0 for all i = j. For the same re
School: Berkeley
Course: Statistical Genomics
we obtain C1 X 2 1 1 2 1 2 = = 2 2 2 2 ) 1 2 1 1 2 1 2 (1 1 2 1 1 2 1 2 1 1 2 1 2 1 2 2 1 2 1 2 2 . (5) Thus x1 1 x2 2 1 (x X ) C1 (x X ) = X 2 (6) 2(1 2 ) x1 1 x2 2 = = x1 1 x2 2 x 1 1 (x212 ) 2 2 1 (x 1 1 ) 1 2 + x2 2 2 2 (7) 2(1 2 ) (x 1 1 )2 2 1
School: Berkeley
Course: Statistical Genomics
Problem 5.3.6 Solution In Example 5.1, random variables N1 , . . . , Nr have the multinomial distribution PN1 ,.,Nr (n 1 , . . . , n r ) = n n p n 1 pr r n 1 , . . . , nr 1 (1) where n > r > 2. (a) To evaluate the joint PMF of N1 and N2 , we dene a new ex
School: Berkeley
Course: Statistical Genomics
The same recursion will also allow us to show that 1 2 (14) E J2 = (3/2)8 1012 + (3/2)6 + (3/2)5 + (3/2)4 + (3/2)3 106 4 1 2 (15) E J1 = (3/2)10 1012 + (3/2)8 + (3/2)7 + (3/2)6 + (3/2)5 + (3/2)4 106 4 1 2 (3/2)10 + (3/2)9 + + (3/2)5 106 (16) E J0 = (3/2)1
School: Berkeley
Course: Statistical Genomics
The complete expression for the joint PDF of Y1 and Y2 is f Y1 ,Y2 (y1 , y2 ) = 12(1 y2 )2 0 y1 y2 1 0 otherwise (9) For 0 y1 1, the marginal PDF of Y1 can be found from f Y1 (y1 ) = 1 f Y1 ,Y2 (y1 , y2 ) dy2 = 12(1 y2 )2 dy2 = 4(1 y1 )3 (10) y1 The compl
School: Berkeley
Course: Statistical Genomics
function err=poissonsigma(a,k); xmin=max(0,floor(a-k*sqrt(a); xmax=a+ceil(k*sqrt(a); sx=xmin:xmax; logfacts =cumsum([0,log(1:xmax)]); %logfacts includes 0 in case xmin=0 %Now we extract needed values: logfacts=logfacts(sx+1); %pmf(i,:) is a Poisson a(i) P
School: Berkeley
Course: Statistical Genomics
Given f X (x) with c = 2/3 and a1 = a2 = a3 = 1 in Problem 5.2.2, nd the marginal PDF f X 3 (x3 ). Filling in the parameters in Problem 5.2.2, we obtain the vector PDF 2 (x 3 1 f X (x) = 0 + x2 + x3 ) 0 x1 , x2 , x3 1 otherwise (1) In this case, for 0 x3
School: Berkeley
Course: Statistical Genomics
The above expression may seem unwieldy and it isnt even clear that it will sum to 1. To simplify the expression, we observe that PX,Y (x, y) = PX,Y,Z (x, y, 5 x y) = PX,Y |Z (x, y|5 x + y) PZ (5 x y) (7) Using PZ (z) found in part (c), we can calculate PX
School: Berkeley
Course: Statistical Genomics
function x=bigpoissonrv(alpha) 0or vector alpha, returns a vector x such that % x(i) is a Poisson (alpha(i) rv et up Poisson CDF from xmin to xmax for each alpha(i) alpha=alpha(:); amin=min(alpha(:); amax=max(alpha(:); %Assume Poisson PMF is negligible +-
School: Berkeley
Course: Statistical Genomics
Problem 5.6.1 Solution (a) The coavariance matrix of X = X 1 X 2 is 4 3 Cov [X 1 , X 2 ] Var[X 1 ] = . 3 9 Var[X 2 ] Cov [X 1 , X 2 ] CX = (1) Y1 1 2 = X = AX. Y2 3 4 (2) (b) From the problem statement, Y= By Theorem 5.13, Y has covariance matrix CY = ACX
School: Berkeley
Course: Statistical Genomics
Unfortunately, the tables in the text have neither (7) nor Q(7). However, those with access to M ATLAB, or a programmable calculator, can nd out that Q(7) = 1 (7) = 1.281012 . This implies that a boat nishes in negative time with probability FW (0) = 1 (1
School: Berkeley
Course: Statistical Genomics
Since the components of J are independent, it has the diagonal covariance matrix 0 0 Var[J1 ] 1 p 0 = Var[J2 ] CJ = 0 I p2 0 0 Var[J3 ] (3) Given these properties of J, nding the same properties of K = AJ is simple. (a) The expected value of K is 1 0 0
School: Berkeley
Course: Statistical Genomics
In fact, these PDFs are the same in that 2 0 x y 1, 0 otherwise. f Y1 ,Y2 (x, y) = f Y3 ,Y4 (x, y) = (16) This implies RY (1, 2) = RY (3, 4) = E[Y3 Y4 ] and that 1 E [Y3 Y4 ] = 0 y 1 2x y d x dy = 0 yx 2 0 y 0 1 dy = 0 1 y 3 dy = . 4 (17) Continuing in th
School: Berkeley
Course: Statistical Genomics
From this model, the vector T = T1 T31 has covariance matrix C T [30] . . C T [1] C T [0] . CT = . . . . . . C T [1] C T [1] C T [0] C T [30] C T [0] . . . . C T [1] (2) If you have read the solution to Quiz 5.8, you know that CT is a symmetric Toe
School: Berkeley
Course: Statistical Genomics
The complete expression is PK 1 ,K 2 (k1 , k2 ) = p 2 (1 p)k2 2 1 k1 < k2 0 otherwise (6) Next we nd PK 1 ,K 3 (k1 , k3 ). For k1 1 and k3 k1 + 2, we have k3 1 PK 1 ,K 3 (k1 , k3 ) = PK 1 ,K 2 ,K 3 (k1 , k2 , k3 ) = k2 = p 3 (1 p)k3 3 (7) k2 =k1 +1 = (k3
School: Berkeley
Course: Statistical Genomics
Problem 5.5.4 Solution Let X i denote the nishing time of boat i. Since nishing times of all boats are iid Gaussian random variables with expected value 35 minutes and standard deviation 5 minutes, we know that each X i has CDF X i 35 x 35 x 35 = (1) FX i
School: Berkeley
Course: Statistical Genomics
Following the same procedure, the marginal PMF of K 2 is k2 1 PK 1 ,K 2 (k1 , k2 ) = PK 2 (k2 ) = k1 = p 2 (1 p)k2 2 (17) k1 =1 = (k2 1) p 2 (1 p)k2 2 (18) Since PK 2 (k2 ) = 0 for k2 < 2, the complete PMF is the Pascal (2, p) PMF PK 2 (k2 ) = k2 1 2 p (1
School: Berkeley
Course: Statistical Genomics
The PDF of Y is 1 f Y (y) = 1 e(yY ) CY (yY )/2 (10) 2 12 1 2 2 e(y1 +y1 y2 16y1 20y2 +y2 +112)/6 = 48 2 (11) Since Y = X 1 , X 2 , the PDF of X 1 and X 2 is simply f X 1 ,X 2 (x1 , x2 ) = f Y1 ,Y2 (x1 , x2 ) = 1 48 2 e(x1 +x1 x2 16x1 20x2 +x2 +112)/6 2
School: Berkeley
Course: Statistical Genomics
Problem 5.6.5 Solution The random variable Jm is the number of times that message m is transmitted. Since each transmission is a success with probability p, independent of any other transmission, J1 , J2 and J3 are iid geometric ( p) random variables with
School: Berkeley
Course: Statistical Genomics
Note that the events A1 , A2 , . . . , An are independent and P A j = (1 p)k j k j1 1 p. (3) Thus PK 1 ,.,K n (k1 , . . . , kn ) = P [A1 ] P [A2 ] P [An ] (4) = p n (1 p)(k1 1)+(k2 k1 1)+(k3 k2 1)+(kn kn1 1) kn n = p (1 p) n (6) To clarify subsequent resu
School: Berkeley
Course: Introductory Probability And Statistics For Busines...
Statistical Independence and Dependence (Denition) Two things are statistically independent if: no matter how the rst one turns out, the chances for the second one remain the same; or no matter how the second one turns out, the chances for the rst one rem
School: Berkeley
Course: Introductory Probability And Statistics For Busines...
Statistics 2 Fall, 2012 Page 1 of 8 pages A line of reasoning. The next three examples introduce the logic underlying tests of signicance. Example 1. ) shows up 17 times. The A die is rolled 60 times. The single dot ( expected number is 10, so the 17 is 7
School: Berkeley
1 1 2 5 3&4 1 2&5 3 4 135 1 4 2 3&5 1 4&5 2 3 154 1&2 4&5 1&2&4 5 3 1&3 4 2&5 1&3&5 4 2 1&4 5 2&3 12 1254 1 2&5 3&4 1352 1425 1 4&5 2&3 1542 1&2 4&5 3 1&2&4&5 1&3 4 5 1&4 1&4 5 3 123 12543 1 2&5 4 13524 14253 1 4&5 3 15423 1&2 5 1&2&4&5 3 1&3 4 5 2 1&4 2
School: Berkeley
Course: Concepts Of Probability
Statistics 134, Section 2, Spring 2010 Instructor: Hank Ibser Lectures: TTh 11-12:30 in 60 Evans. Oce Hours: TTh 9:30-10:30 and 3:40-4:30, in 349 Evans Hall. Other times/places by appt. Oce Phone: 642-7495 Email: hank@stat.berkeley.edu Text: Probability b
School: Berkeley
Course: Introductory Probability And Statistics For Busines
UNIVERSITY OF CALIFORNIA Department of Economics Econ 100B Course Outline Spring 2012 Economics 100B Economic Analysis: Macroeconomics Professor Steven A. Wood Administrative Detail: Class Sessions: Tuesdays and Thursdays, 3:30 p.m. 5:00 p.m., 2050 Valley
School: Berkeley
Course: Introductory Probability And Statistics For Busines
Statistics 21, Section 1, Spring 2012 Instructor: Hank Ibser Lectures: MWF 9-10, 155 Dwinelle Email: hank@stat.berkeley.edu Office Hours: MW 10:10-11, 1:10-2, in 349 Evans Hall. Text: Statistics, 4rd ed. by Freedman, Pisani, Purves, Well cover most of cha
School: Berkeley
Stat 150 Spring 2015 Syllabus Available online at http:/www.stat.berkeley.edu/~sly/Stat150Spring2015Syllabus.pdf Instructor: Allan Sly GSI: Jonathan Hermon Course Webpage: http:/www.stat.berkeley.edu/~sly/STAT150.html Class Time: MWF 12:00 - 1:00 PM in ro
School: Berkeley
Course: Concepts Of Probability
Stat 134: Concepts of Probability Instructor: Michael Lugo e-mail: mlugo at stat dot berkeley dot edu Office: 325 Evans Office hours: TBA GSI: TBA. Class schedule: Lectures Monday, Wednesday, and Friday, from 12:10 PM to 1:00 PM, 60 Evans. There are two o
School: Berkeley
Course: Concepts In Computing With Data
STAT$133:$Concepts$in$Computing$with$Data$ ! $ Instructor:$Deborah!Nolan,!395!Evans,$ deborah_nolan@berkeley.edu! OH:$Wed!1:30>3:30! $ GSI:!Bradly,!Christine,!Inna! OH:!Mon!10>11,!5>6,!Tue!2>4,!Wed!4>5,!and!Thu!5>7$ ! Lectures:!Tue/Thu!12:30>2pm;!2050!VLS
School: Berkeley
Course: Introduction To Statistics
STAT 2 Lec Sec 1: Fall 2014 (Course Control Number: 87303) INSTRUCTOR: Ann Kalinowski Email address ann.kalinowski@berkeley.edu Office: 449 Evans Hall OFFICE HOURS: TTh 11- noon, 1:30pm-3pm I will usually be in my office all day, except for 1 hr lunch, un
School: Berkeley
Course: Introductory Probability And Statistics For Busines
Schedule for Stat 21, Fall 2013 Note: Chapter readings are from FPP, and SG refers to Professor Philip Starks free online text SticiGui. notes by RP indicates Professor Roger Purves notes on chance variables, which will be posted on Canvas later. Week 1 (
School: Berkeley
Course: Introductory Probability And Statistics For Busines
STAT 21 Syllabus Course Information: Instructor: Shobhana Murali Stoyanov, shobhana@stat.berkeley.edu Class time: TuTh 2-3:30P, F295 Haas Office hours: W: 11-1P & by appointment, 325 Evans Text: Statistics, 4th ed., by Freedman, Pisani, and Purves. Supple
School: Berkeley
Statistics 21, Section 1, Spring 2010 Instructor: Hank Ibser Lectures: TTh 2-3:30pm, 2050 VLSB Email: hank@stat.berkeley.edu Oce Phone: 642-7495 Oce Hours: TuTh 9:30-10:30, 3:40-4:30, in 349 Evans Hall. Other times/places by appointment. Text: Statistics,
School: Berkeley
Course: Sampling Surveys
STAT152: Survey Sampling, Fall 2005 http:/www.stat.berkeley.edu/users/hhuang/STAT152.html Homework & lab assignment SYLLABUS Haiyan Huang, 317 Evans, (510)-642-6433 hhuang@stat.berkeley.edu Office Hours: M 4:00pm-5:00pm; T 3:00pm-4:00pm; or by appoi