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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: 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 ,
School: Berkeley
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 (
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 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: 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
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: 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
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: 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
School: Berkeley
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
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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
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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: 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
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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
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
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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
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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
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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
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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
School: Berkeley
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
School: Berkeley
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
School: Berkeley
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
School: Berkeley
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/
School: Berkeley
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
School: Berkeley
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
School: Berkeley
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
School: Berkeley
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
School: Berkeley
Course: Concepts Of Probability
2 Repeated Trials and Sampling This chapter studies a mathematical model for repeated trials, each of which may result in some event either happening or not happening. Occurrence of the event is called success, and non-occurrence called failure. For insta
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 Midterm Review Format Sun 10/13 Read the problems listed below. Then try those that you are
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 6: Dependence Chapter 6 Table of Contents Chapter 6: Dependence . 1 Chapter 6 Table
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 5: Continuous Joint Distributions Chapter 5 Table of Contents Chapter 5: Continuous
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 4: Continuous Distributions Chapter 4 Table of Contents Chapter 4: Continuous Distri
School: Berkeley
Course: Linear Modelling: Theory And Applications
Fall 2013 Statistics 151 (Linear Models) : Lecture Twenty Six Aditya Guntuboyina 05 December 2013 1 Classication Trees We looked at regression trees in the class. The idea behind classication trees is similar. The classication tree is constructed top down
School: Berkeley
Course: Linear Modelling: Theory And Applications
Fall 2013 Statistics 151 (Linear Models) : Lecture Twenty Two Aditya Guntuboyina 14 November 2013 We will again look at tting the logistic regression model to data. But before that, let us digress a little and take a brief look at weighted least squares 1
School: Berkeley
Course: Linear Modelling: Theory And Applications
Fall 2013 Statistics 151 (Linear Models) : Lecture Twenty One Aditya Guntuboyina 12 November 2013 1 Generalized Linear Models We have n observations on a response variable y1 , . . . , yn and on each of p explanatory variables xij for i = 1, . . . , n and
School: Berkeley
Course: Linear Modelling: Theory And Applications
Fall 2013 Statistics 151 (Linear Models) : Lecture Twenty Aditya Guntuboyina 7 November 2013 1 Generalized Linear Models We have so far studied linear models. We have n observations on a response variable y1 , . . . , yn and on each of p explanatory varia
School: Berkeley
Course: Linear Modelling: Theory And Applications
Fall 2013 Statistics 151 (Linear Models) : Lecture Nineteen Aditya Guntuboyina 5 November 2013 1 Criteria Based Variable Selection We have so far looked at the following criteria. 1. Adjusted R2 2. AIC 3. BIC 4. Mallowss Cp 2 Mallowss Cp Mallows Cp is den
School: Berkeley
Course: Linear Modelling: Theory And Applications
Fall 2013 Statistics 151 (Linear Models) : Lecture Eighteen Aditya Guntuboyina 31 October 2013 1 Criteria Based Variable Selection If there are p explanatory variables, then there are 2p possible linear models. In criteria-based variable selection, we t a
School: Berkeley
Course: Linear Modelling: Theory And Applications
Fall 2013 Statistics 151 (Linear Models) : Lecture Seventeen Aditya Guntuboyina 29 October 2013 1 Variable Selection Consider a regression problem with a response variable y and p explanatory variables x1 , . . . , xp . Should we just go ahead and t a lin
School: Berkeley
Course: Linear Modelling: Theory And Applications
Fall 2013 Statistics 151 (Linear Models) : Lecture Fifteen Derek Bean 22 October 2013 1 Recap Let (x1 , y1 ), . . . , (xn , yn ) be n predictor-response pairs; let X be the n (p + 1) design matrix with ith row (1, xi )T (so an intercept is included) and l
School: Berkeley
Course: Linear Modelling: Theory And Applications
Fall 2013 Statistics 151 (Linear Models) : Lecture Sixteen Derek Bean 24 October 2013 We went over some diagnostic tools, mostly graphical, for checking the reasonableness of certain key assumptions of the linear model: Normality are the errors normally
School: Berkeley
Course: Linear Modelling: Theory And Applications
Fall 2013 Statistics 151 (Linear Models) : Lecture Thirteen Aditya Guntuboyina 15 October 2013 1 Regression Diagnostics For regression diagnostics, we need to know about the following quantities: 1. Leverage 2. Standardized or Studentized Residuals 3. Pre
School: Berkeley
Course: Linear Modelling: Theory And Applications
Fall 2013 Statistics 151 (Linear Models) : Lecture Eleven Aditya Guntuboyina 03 October 2013 1 One Way Analysis of Variance Consider the model yij = i + eij for i = 1, . . . , t and j = 1, . . . , ni where eij are i.i.d normal random variables with mean z
School: Berkeley
Course: Linear Modelling: Theory And Applications
Fall 2013 Statistics 151 (Linear Models) : Lecture Seven Aditya Guntuboyina 19 September 2013 1 Last Class We looked at 1. Fitted Values: Y = X = HY where H = X(X T X)1 X T Y . Y is the projection of Y onto the column space of X. 2. Residuals: e = Y Y = (
School: Berkeley
Course: Linear Modelling: Theory And Applications
Fall 2013 Statistics 151 (Linear Models) : Lecture Twelve Aditya Guntuboyina 10 October 2013 1 Regression Diagnostics We now talk about regression diagnostics. I follow the treatment in Christensens book (Plane Answers to Complex Questions), Chapter 13 ve
School: Berkeley
Course: Linear Modelling: Theory And Applications
Fall 2013 Statistics 151 (Linear Models) : Lecture Six Aditya Guntuboyina 17 September 2013 We again consider Y = X + e with Ee = 0 and Cov(e) = 2 In . is estimated by solving the normal equations X T X = X T Y . 1 The Regression Plane If we get a new sub
School: Berkeley
Course: Linear Modelling: Theory And Applications
Statistics 151a - Linear Modelling: Theory and Applications Adityanand Guntuboyina Department of Statistics University of California, Berkeley 29 August 2013 1 / 25 The Regression Problem This class deals with the regression problem where the goal is to u
School: Berkeley
Course: Linear Modelling: Theory And Applications
Fall 2013 Statistics 151 (Linear Models) : Lecture Four Aditya Guntuboyina 10 September 2013 1 Recap 1.1 The Regression Problem There is a response variable y and p explanatory variables x1 , . . . , xp . The goal is understand the relationship between y
School: Berkeley
Course: Linear Modelling: Theory And Applications
Fall 2013 Statistics 151 (Linear Models) : Lecture Five Aditya Guntuboyina 12 September 2013 1 Least Squares Estimate of in the linear model The linear model is with Ee = 0 and Cov(e) = 2 In Y = X + e where Y is n 1 vector containing all the values of the
School: Berkeley
Course: Linear Modelling: Theory And Applications
Fall 2013 Statistics 151 (Linear Models) : Lecture Three Derek Bean 05 September 2013 1 Linear Algebra Review, contd Result: for matrix A, rank(A) + dim(K(A) = no. of columns in A. Denition: Matrix A is full rank if rank(A) = no. of columns in A (i.e. d
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Course: Introduction To Time Series
Spring 2013 Statistics 153 (Time Series) : Lectures Twenty Four Aditya Guntuboyina 22 April 2014 1 Spectral Distribution Function and Spectral Density Let cfw_Xt be a stationary sequence of random variables and let X (h) = cov(Xt , Xt+h ) denote the auto
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 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: Introduction To Statistics
Stat 2 Administrative stuff lecture 2 Things you need to know Lecture notes will be posted after class on bcourses (NOT bspace)! Access bcourses: https:\bcourses.berkeley.edu Corrections from last time My office is 449 Evans Grading scheme is as I a
School: Berkeley
Course: INTRO TO STAT
STAT 20 Section Plan Thursday, March 22, 2012 A friend of mine has an unfair coin. He ipped the coin 15 times and observed 13 heads and 2 tails. Now, Im wondering how biased this coin is. In other words, what proportion of times will this coin ip a head?
School: Berkeley
Course: INTRO TO STAT
# vector to represent the biased coin coin <- c(rep(1,8), rep(0,2) # generate a sample of 15 flips n <- 15 my.flips <- sample(coin, size = n, replace = TRUE) # calculate the sample statistics prop.head <- mean(my.flips) se <- sd(my.flips) / sqrt(n) # che
School: Berkeley
Course: INTRO TO STAT
STAT 20 Section February 23, 2012 Chapter 2 Review Exercises (FPP): 1 2 3
School: Berkeley
Course: INTRO TO STAT
Stat 20 Section Feb 16, 2012 1. From Tuesdays section: plotting and regression in R The Crime dataset is at: http:/rss.acs.unt.edu/Rdoc/library/Ecdat/html/Crime.html google data sets for Econometrics >install.packages("Ecdat") >library(Ecdat) >data(Crime)
School: Berkeley
Course: INTRO TO STAT
Stat 20 Section Plan Feb 14, 2012 1. R System Good-to-Knows: - remember:getwd(),setwd(C:/Boriska/Stat20/) (Windows example) common mistake: dont try to use tilde ~ in Windows to begin the file path - make sure youre in the right directory! - list files in
School: Berkeley
Course: INTRO TO STAT
# Tuesday, March 6 # Part (a) # Out of ten tickets, possible net gains would like net.gain <- c(20, rep(5,2), rep(-5,7) # To make the 'big box', just repeat this vector 500 to represent all 5000 # tickets box.model <- rep(net.gain, 500) # Part (c) box.m
School: Berkeley
Course: INTRO TO STAT
# to simulate uniformly distributed data, we can use the function sample() n <- 10000 die <- sample(1:6, size = n, replace = TRUE) #calculate the mean mean(die) #proportion of sixes, compare to 1/6 mean(die = 6) #calculate the probability of throwing mo
School: Berkeley
Course: INTRO TO STAT
Stat20 Section Plan 3/6 1. FPP Problems: Ch16, Set A, #4-5 2. Suppose a fundraising game is being held, where thousands of tickets (>5000) are sold. Each ticket costs $5, and the purchaser of the ticket wins a prize depending on what is printed on the tic
School: Berkeley
Course: INTRO TO STAT
Stat20 Section Plan 3/8 1. a) Use R to check what percent of the area below the curve is within two SDs of the mean on a bell curve with mean=0, SD=1. (The bell curve with mean=0, SD=1 is called the standard bell curve.) In other words, check what percent
School: Berkeley
Course: INTRO TO STAT
Stat20 Section Plan 3/6- Solution 2. Suppose a fundraising game is being held, where 5000 tickets are sold. Each ticket costs $5, and the purchaser of the ticket wins a prize depending on what is printed on the ticket. The odds are as follows: one-tenth o
School: Berkeley
Course: INTRO TO STAT
Points: - You can go to anyones oce hour. - Demo for online text book. Density Plots Density Plot, a smoothed version of a histogram. Area still corresponds to percentages. Qualitative Data HIV Clinic Survey about Anonymous vs Condential Testing. Collecte
School: Berkeley
Course: INTRO TO STAT
Surveys Design of the survey The survey itself is a measurement, if it is poorly worded, then you can get biases. Design of the sample Who you give the survey to also matters. All slides below are thanks to Prof Nolan! Compare: Do you agree or disagree wi
School: Berkeley
Course: INTRO TO STAT
Some warning~ This is the beginning of formal analysis, i.e. the abstract stu that people nd hard about statistics! Its really quite elegant~ Review Box model An abstraction for many random events, e.g. coin toss is like a draw from a box with 2 tickets,
School: Berkeley
Course: INTRO TO STAT
Week 2 Section Plan January 30, 2012 - Please solve in pairs, talk about your reasoning and give examples to support the TRUE/FALSE portion. - Work on these for 35 minutes then well go over the solutions using the last 15 minutes. SD calculation exercise:
School: Berkeley
Course: INTRO TO STAT
Correction Correlation Formula: 1 r= n i=1 Xi X Yi Y SDX SDY The regression formula Yi Y SDy =r Xi X SDx where r is the correlation and Y and X are the mean for X and Y respectively. SDy and SDx are the SD for X and Y respectively. Yi Yi Xi X =r SDy +
School: Berkeley
Course: INTRO TO STAT
Review Chat about midterm, when to review? We talked about how to collect data! Sampling, when does which make sense. But what happens to our analysis when we get dierent samples? Our analysis based on dierent samples might be dierent. Our sample may not
School: Berkeley
Course: INTRO TO STAT
Start Studying! Practice midterm should be out next week HW4 is still due soon Check out the syllabus Review How to quantify how likely it is to get a bad sample? just simulate it and count! Review Practice Using the class survey data, how do I quantify h
School: Berkeley
Course: INTRO TO STAT
What statistics cannot tell you http:/economix.blogs.nytimes.com/2012/02/17/interracialcouples-who-make-the-most-money/ Review Terms What are your observation units, i.e. basic unit on which a measurement is taken (who or what are you measuring from)? Who
School: Berkeley
Course: INTRO TO STAT
Clarication My bad grammar.big mistake! Someones k standard deviations away from the mean means their X value is k in standard units. Review Correlation: only linear relationships Regression: Summary for scatter plot, like the mean is for a histogram Pred
School: Berkeley
Course: INTRO TO STAT
Some points Be careful with compound functions Use the script plotting document up! Homework policy. Report Demo Example thanks to Professor Nolan: Report Demo Example thanks to Professor Nolan: Report Key Tell me an interesting story! - Ask yourself why
School: Berkeley
Course: INTRO TO STAT
Review Principles: 1) Show the data clearly 2) Facilitate Comparisons 3) Make the graph rich in information and interesting. Review Where are we now? Comparing two dierent quantitative variables Do tall people tend to make more money? Do higher SAT scores
School: Berkeley
Course: INTRO TO STAT
Numerical Representation: Measures for Spread Why bother about spread? 2 options for wages: Job A: at the end of the month, you ip a fair coin, and you get double salary or nothing Job B: at the end of the month, you get your monthly salary. Which one is
School: Berkeley
Course: INTRO TO STAT
Points There is more to the syllabus than just the grade breakdown. - To download R, look at the syllabus. - To nd supportive reading, look at the syllabus. - To nd the link to R videos, look at the syllabus. Some Fun Graphs http:/www.wired.com/wiredscien
School: Berkeley
Course: INTRO TO STAT
Some details I left out If you want to switch sections. Reading materials and homework. Not posting notes before class Review Data types: Quantitative: Graphs: stripchart, histogram Summary Stat: mean, median, mode Qualitative: to be continued! Numerical
School: Berkeley
Course: INTRO TO STAT
Stat 20 Lectures January 18, 2012 Handout and Syllabus Im NOT Ani or Bin. Read the Syllabus online! Waitlist and other enrollment issues No section this week. Fill out the handout PLEASE! Some questions are intentionally vague Complaints What I hear at th
School: Berkeley
Course: STATISTICS
Summation and Correlation The correlation coecient r can be written either 1 n (xi x) (yi y ) n i=1 SDx SDy n i=1 1 n or xi y i xy SDx SDy The proof is as follows: 1 n (xi x) (yi y ) n i=1 SDx SDy = = = = n 1 n SDx SDy 1 SDx SDy 1 n n i=1 n 1 = n SDx SDy
School: Berkeley
Course: STATISTICS
Summation, Average, and Standard Deviation Denitions and Formulas Lists of numbers are often written as xi . Each number on the list is one of these xi values. Thus the list 1, 4, 6 would have x1 = 1, x2 = 4, and x3 = 6. Here are a few formulas we will us
School: Berkeley
Course: INTRODUCTION TO PROBABILITY AND STATISTICS
v ~ ~- Jk_ Yu~ ~-+- l J& c+-e ~ & ~-~-~ sh(/cfw_1 ~ ~/s /U~ (l[J_;_I_o_ _ ;/lk _ ~1J~- I/J10d? /178 /() if_ ( ;1 _ :-.mJe_- _ )_fL~ft-r-~fce ~-('~ q~- - - - 01~ jv;/ how O!c-1-utA (c-r~Aud . -+-gj_ 1/t_Q - - - - tJ t1rlf;7; -Jt&z ;v; -~- - - - - - - - -
School: Berkeley
Course: Game Theory
Game Theory, Alive Anna R. Karlin and Yuval Peres Draft January 20, 2013 Please send comments and corrections to karlin@cs.washington.edu and peres@microsoft.com i We are grateful to Alan Hammond, Yun Long, Gbor Pete, and Peter a Ralph for scribing early
School: Berkeley
School: Berkeley
AverageSoFar 58.33 58.00 57.67 57.33 57.33 57.33 57.00 56.83 56.67 56.67 56.50 56.33 56.33 56.33 56.17 56.00 56.00 55.67 55.67 55.50 55.33 55.33 55.33 55.33 55.17 55.00 54.83 54.67 54.50 54.33 54.33 54.00 54.00 53.83 53.83 53.67 53.67 53.50 53.33 53.33 53
School: Berkeley
Stat 20: Intro to Probability and Statistics Lecture 24: 2 Testing Tessa L. Childers-Day UC Berkeley 5 August 2014 Recap Test for Distribution Test for Independence Recap: Hypothesis Testing Steps in Hypothesis Testing: 1 State the hypotheses Null: The di
School: Berkeley
Stat 20: Intro to Probability and Statistics Lecture 23: Two Sample Testing Tessa L. Childers-Day UC Berkeley 4 August 2014 Recap Surveys Experiments Recap: Hypothesis Testing Steps in Hypothesis Testing: 1 State the hypotheses Null: The dierence between
School: Berkeley
Stat 20: Intro to Probability and Statistics Lecture 25: Pitfalls and Limits In Testing Tessa L. Childers-Day UC Berkeley 6 August 2014 Recap Interpreting Signicance Data Snooping Role of Model Questions Matter Recap: Hypothesis Testing Steps in Hypothesi
School: Berkeley
Stat 20: Intro to Probability and Statistics Lecture 22: Hypothesis Testing Tessa L. Childers-Day UC Berkeley 31 July 2014 Recap Examples Recap: Hypothesis Testing Steps in Hypothesis Testing: 1 State the hypotheses Null: The dierence between the sample a
School: Berkeley
Stat 20: Intro to Probability and Statistics Lecture 21: Intro to Hypothesis Testing Tessa L. Childers-Day UC Berkeley 30 July 2014 Recap Natural Questions Hypothesis Testing Example Recap: From Samples to Boxes Spent the past 3 days reasoning from a samp
School: Berkeley
Stat 20: Intro to Probability and Statistics Lecture 20: Condence Intervals for Averages Tessa L. Childers-Day UC Berkeley 29 July 2014 Recap Known Box Unknown Box SE Summary Recap: 0-1 Box Yesterday we saw a 0-1 box: Composition unknown Took SRS from box
School: Berkeley
Stat 20: Intro to Probability and Statistics Lecture 19: Condence Intervals for Percentages Tessa L. Childers-Day UC Berkeley 28 July 2014 Recap Unknown Box Condence Intervals Examples By the end of this lecture. You will be able to: Estimate a 0-1 box mo
School: Berkeley
Stat 20: Intro to Probability and Statistics Lecture 18: Simple Random Sampling Tessa L. Childers-Day UC Berkeley 24 July 2014 Recap Simple Random Samples EV and SE Examples By the end of this lecture. You will be able to: Draw box models for real-world s
School: Berkeley
Stat 20: Intro to Probability and Statistics Lecture 17: Using the Normal Curve with Box Models Tessa L. Childers-Day UC Berkeley 23 July 2014 Todays Goals Probability Histograms Probability Histogram Normal Curve Central Limit Theorem By the end of this
School: Berkeley
Stat 20: Intro to Probability and Statistics Lecture 16: More Box Models Tessa L. Childers-Day UC Berkeley 22 July 2014 Todays Goals EV and SE Normal Curve Classifying and Counting By the end of this lecture. You will be able to: Determine what we expect
School: Berkeley
Stat 20: Intro to Probability and Statistics Lecture 13: Binomial Formula Tessa L. Childers-Day UC Berkeley 14 July 2014 Todays Goals Recap Counting Calculating Probabilities Examples By the end of this lecture. You will be able to: Calculate the ways an
School: Berkeley
Stat 20: Intro to Probability and Statistics Lecture 15: Law of Averages Tessa L. Childers-Day UC Berkeley 21 July 2014 Todays Goals Recap Law of Averages Box Models By the end of this lecture. You will be able to: Relate the law of averages to the deniti
School: Berkeley
Stat 20: Intro to Probability and Statistics Lecture 14: Exam 1 Review Tessa L. Childers-Day UC Berkeley 15 July 2014 Exam 1 Guidelines Material Covered Q&A Details Wednesday, 16 July 2014 In lecture, this room Lasts 80 minutes (9:10am to 10:30am) Worth 3
School: Berkeley
Stat 20: Intro to Probability and Statistics Lecture 12: More Probability Tessa L. Childers-Day UC Berkeley 10 July 2014 Todays Goals Recap More Rules and Techniques Examples By the end of this lecture. You will be able to: Use the theory of equally likel
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: 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
School: Berkeley
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
School: Berkeley
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: Concepts Of Probability
Stat 134 Study Group Fac: Professor Pitman SGL: Mike Leong, mleong@berkeley.edu Loc: 11-12 pm, 201A Chvez Community through Academics and Leadership Chapter 2: Repeated Trials and Sampling Chapter 2 Table of Contents Chapter 2: Repeated Trials and Samplin
School: Berkeley
Course: Concepts Of Probability
Stat 134 Final Exam Spring 2013 Instructor: Allan Sly Name: SID: There are 8 questions worth a total of 67 points plus 7 points from bonus questions. The maximum score will be 60 and higher scores will be truncated. Attempt all questions and show your wor
School: Berkeley
Course: Concepts Of Probability
Stat 134 Final Exam Spring 2013 Instructor: Allan Sly Name: SID: There are 8 questions worth a total of 76 points - the maximum score will be 70 and higher scores will be truncated. Attempt all questions and show your working. Answer the questions in the
School: Berkeley
Course: Concepts Of Probability
Stat 134 Final Exam Spring 2013 Instructor: Allan Sly Name: SID: There are 8 questions worth a total of 76 points - the maximum score will be 70 and higher scores will be truncated. Attempt all questions and show your working. Answer the questions in the
School: Berkeley
Course: INTRODUCTION TO PROBABILITY AND STATISTICS
Practice Midterm 2 1. We surveyed 100 women about their weights and heights, and got the following results; average height = 64 inches, average weight = 140 pounds, SD = 4 inches SD = 15 pounds The correlation coecient r between the heights and weights wa
School: Berkeley
Course: INTRODUCTION TO PROBABILITY AND STATISTICS
MIDTERM 2 04/16/2014 Olena Blumberg Name: GSI and Section #: Show your work for all the problems. Good luck! 1. We surveyed 100 men about their weights and heights, and got the following results: average height = 69 inches, average weight = 170 pounds, SD
School: Berkeley
Course: INTRODUCTION TO PROBABILITY AND STATISTICS
FINAL EXAM 05/14/2014 Olena Blumberg Name: GSI and Section #: Show your work for all the problems. Good luck! 1. In a certain school district, about 7% of the students are homeschooled, and the remaining 93% go to conventional schools. The average SAT sco
School: Berkeley
Course: INTRODUCTION TO PROBABILITY AND STATISTICS
FINAL EXAM 05/14/2014 Olena Blumberg Name: GSI and Section #: Show your work for all the problems. Good luck! 1. [5 pts] A researcher is interested in whether more sleep boosts the immune system. So she calls a random sample of 400 people and asks them ho
School: Berkeley
Course: INTRODUCTION TO PROBABILITY AND STATISTICS
FINAL EXAM 05/14/2014 Olena Blumberg Name: GSI and Section #: Show your work for all the problems. Good luck! 1. In a certain school district, about 7% of the students are homeschooled, and the remaining 93% go to conventional schools. The average SAT sco
School: Berkeley
Course: INTRODUCTION TO PROBABILITY AND STATISTICS
Practice Midterm 1 1. According to an observational study done at Kaiser Permanente in Walnut Creek, California, users of oral contraceptives have a higher rate of cervical cancer than non-suers, even after adjusting for age, educations, marital status, r
School: Berkeley
STATISTICS 21 Fall 2012 S. M. Stoyanov MIDTERM 1 Score:[ /60] Please show ALL WORK AND REASONING for ALL the problems.You may NOT use a programmable calculator for this quiz. Do NOT ROUND the numbers in the middle of a problem. In general, unless asked to
School: Berkeley
STATISTICS 21 Fall 2012 S. M. Stoyanov MIDTERM 2 Score:[ Name: /60] SID: Section: Please circle your sections GSI: Tina Ansari Nathan Cheung Andrew Kwong Nazret Weldeghiorgis Susannah Lee Arie Wong Please show ALL WORK AND REASONING for ALL the problems.Y
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Statistics 21 Fall 2012 Shobhana M. Stoyanov Midterm 2 Score:[ Name: /60] SID: Section: Please circle your sections GSI: Tina Ansari Nathan Cheung Andrew Kwong Nazret Weldeghiorgis Susannah Lee Arie Wong Please show ALL WORK AND REASONING for ALL the prob
School: Berkeley
Statistics 21 Fall 2012 Shobhana M. Stoyanov Midterm 1: Answers Score:[ /60] Please show ALL WORK AND REASONING for ALL the problems.You may NOT use a programmable calculator for this quiz. Do NOT ROUND the numbers in the middle of a problem. In general,
School: Berkeley
STATISTICS 21 FALL 2013 S. M. Stoyanov MIDTERM 2: solutions Score:[ /60] 1. A fair coin is tossed 10 times. Write down the chance of getting exactly 2 heads in the rst 5 tosses, and exactly 1 head in the next 5 tosses. (3 points) Version 2:A fair coin is
School: Berkeley
STATISTICS 21 Fall 2012 S. M. Stoyanov MIDTERM 2 : Solutions Score:[ 1. Use the box 0 0 0 0 0 1 /60] to answer the following questions. Circle the appropriate option, and EXPLAIN your answer. (3 points each) (a) Four draws are made at random with replacem
School: Berkeley
Statistics 21 Fall 2013 Shobhana M. Stoyanov Midterm 1 : Solutions (Both versions) Score:[ Page Score = /60] /15 1. You can nd a list of the CEOs with the highest compensations on the internet at various sites. Interestingly, the list seems to be site-dep
School: Berkeley
School: Berkeley
Stat 20 Fall 06 A. Adhikari ANSWERS TO PRACTICE QUESTIONS FOR THE FINAL 1. The box has 155 tickets. Each ticket has two parts: the left side shows the 1/0 that will be the result if the patient gets assigned to the treatment group, and the right side show
School: Berkeley
Stat 20 Fall 06 A. Adhikari PRACTICE QUESTIONS FOR THE FINAL Important: Some of the problems below are standard applications of the techniques of the class, and others require a little more thought to decide which technique, if any, to use. The focus in t
School: Berkeley
Course: Concepts Of Probability
UNIVERSITY OF CALIFORNIA, BERKELEY DEPARTMENT OF STATISTICS STAT 134: Concepts of Probability Spring 2014 Instructor: Antar Bandyopadhyay Solution to the Final Examination 1. State whether the following statements are true or false. Write brief reasons su
School: Berkeley
Course: Concepts Of Probability
UNIVERSITY OF CALIFORNIA, BERKELEY DEPARTMENT OF STATISTICS STAT 134: Concepts of Probability Spring 2014 Instructor: Antar Bandyopadhyay Solution to the Midterm Examination 1. A point (X, Y ) is randomly selected from the following nite set of points on
School: Berkeley
Course: Concepts Of Probability
UNIVERSITY OF CALIFORNIA, BERKELEY DEPARTMENT OF STATISTICS STAT 134: Concepts of Probability Spring 2014 Instructor: Antar Bandyopadhyay Practice Final Examination (I) Date Given: April 25, 2014 Duration: 180 minutes Total Points: 100 Note: There are ten
School: Berkeley
Course: Concepts Of Probability
UNIVERSITY OF CALIFORNIA, BERKELEY DEPARTMENT OF STATISTICS STAT 134: Concepts of Probability Spring 2014 Instructor: Antar Bandyopadhyay Practice Final Examination (II) Date Given: April 25, 2014 Duration: 180 minutes Total Points: 100 Note: There are te
School: Berkeley
Course: Concepts Of Probability
UNIVERSITY OF CALIFORNIA, BERKELEY DEPARTMENT OF STATISTICS STAT 134: Concepts of Probability Spring 2014 Instructor: Antar Bandyopadhyay Practice Midterm Examination Date Given: March 10, 2014 Duration: 80 minutes Total Points: 60 Note: There are ve prob
School: Berkeley
Course: Game Theory
Stat 155 Midterm Practice Solutions Problems: Attempt all questions and show your working - solutions without explanation will not receive full credit. One double sided sheets of notes are permitted. Q 1 Find the value and optimal strategy of the followin
School: Berkeley
Course: Game Theory
Stat 155 Midterm Spring 2014 Name: SID: This exam has 5 problems and a total of 75 points. Attempt all questions and show your working - solutions without explanation will not receive full credit. One double sided sheets of notes are permitted. Answer que
School: Berkeley
Course: STATISTICS
Stat 20 Quiz 5 April 23, 2014 Name: _ Section: 101, 102, 103, 104 105, 106, 107, 108 SOLUTIONS 8 points possible Part 1 Show all work and put a box around your answer. Provide explanations when youre asked. 1. A recent survey estimated the US per capita c
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
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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
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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
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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:
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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
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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!
School: Berkeley
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 Probability
HW 11: 5.2 (5, 6, 10, 12, 16) 5.3 (6, 8, 12) 5.2 5 Let X ~ Exp ( ) and Y ~ Exp ( ) . Find P(Y 1 X ) . 3 y = x/3 x = 3y Method 1: Integrate over x P(Y X ) 1 3 f x/3 X ,Y ( x, y )dydx e Region x e y dydx e 0 0 0 x x/3 e dydx 0 0 y 0 e x P(Y x / 3)
School: Berkeley
Course: Concepts Of Probability
HW 10: 4.6 (1, 2, 3) 5.1 (2, 4, 6, 7, 9) 4.6 1 Suppose X i ~ iid N ( 0, 2 52 ) for i 1,4 . a) Find the probability that the 1st arrival is before 10. P( X (1) 10) 1 P( X (1) 10) 1 [ P( X 10)]n 1 [ P(Z 2)]4 1 [(2)]4 b) Find the probability that some of th
School: Berkeley
Course: Concepts Of Probability
HW 1: 1.1 (5, 8) 1.2 (2, 3) 1.3 (12, 13, 14, 15) 1.1 5 Draw 2 cards from a standard deck without replacement. Let Ai be the event that the ith card is an ace. a) Find the number of ordered pairs. # of ordered pairs (n)k (52)2 52 51 b) Find the probabilit
School: Berkeley
Course: Concepts Of Probability
HW 2: 1.4 (5, 6, 7, 8, 10, 12) 1.5 (4, 5) 1.4 5 Let Ai be the event that the ith urn is selected. a) Draw a Bayes tree. See diagram. b) Label the following probabilities in the tree. Unconditional: P( A1 ), P( A1 ) Conditional: P( B | A1 ), P(W | A1 ), P
School: Berkeley
Course: Concepts Of Probability
HW 3: 1.6 (5, 6, 7, 8) 2.1 (4, 6, 10, 12) 1.6 5 Suppose U ~ Unif (1, N 365) . Select n numbers with replacement. Let pn = the probability of getting a duplicate with the 1st selected number. Thus 1 pn = the probability that the 1st number is not duplicat
School: Berkeley
Course: Concepts Of Probability
HW 7: 3.4 (8, 12, 14, 17, 18) 3.5 (9, 10, 15) 3.4 8 In a game of craps, let X0 be the 1st sum thrown. The value of X0 is defined as the point. If X0 = 7 or 11, then player wins immediately. If X0 = 2, 3, or 12, then player loses immediately. If X0 = 4, 5
School: Berkeley
Course: Concepts Of Probability
HW 6: 3.2 (13, 14, 16, 17, 22) 3.3 (8, 13, 14) 3.2 13 Roll a fair die 10 times. Let U i ~ Unif (1, k 6) , which is the value of the ith roll. Find the expectation of each of the following random variables: a) Let X = sum of the n 10 rolls. n X U i i 1 1
School: Berkeley
Course: Concepts Of Probability
HW 4: 2.2 (5, 6, 12, 13) 2.4 (5, 7, 8, 9) 2.2 5 Bet a dollar on roulette 25 times. The probability of winning is 18/38 and the payoff is 1:1. Let X = # of games won. Find the probability of not losing any money. X ~ Bin (n 25, p 18 / 38) 18 225 18 20 5 6
School: Berkeley
Course: Concepts Of Probability
HW 5: 2.5 (3, 6, 8, 12) 3.1 (4, 8, 13, 14) 2.5 3 From a standard deck of cards, divide 52 cards evenly among 4 players. Let X = # of aces that 1st player has. Find the probability of each of the following events: a) 1st player has all the aces Aces Non-a
School: Berkeley
Course: Concepts Of Statistics
Chapter 10 1 Consider the situation where the average response Y for conditions A and B are as follows: Not A 10 12 Average Y Not B B A 20 22 Under this situation, for any given state of condition A (A or Not A), B is associated with an increase in the av
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Course: Concepts In Computing With Data
Stat 133, Fall 2014 Homework 7: KML Due Thursday, November 13 at 11:55pm on bSpace Your task is to create a Google Earth display of the infant mortality and population for countries around the world. Google Earth uses a particular dialect of XML called KM
School: Berkeley
Course: Concepts In Computing With Data
Stat 133, Fall 2014 Homework 2: Graphics with Trac Data Due on bSpace by Thursday, Sept 18, 11:55pm Directions: Turn in a plain text le containing the R commands you use to solve the following problems. The le should be named LastnameFirstnameHW2 with eit
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Course: Concepts In Computing With Data
Stat 133, Fall 2014 Homework 6: Text Manipulation: Creating Spam-related Variables Due: Thursday, Wednesday Nov 6, 11:55pm About the Data For this homework, you will be creating some basic spam lters for e-mail. The emails you will use for this assignment
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Course: Concepts In Computing With Data
Stat 133, Fall 2014 Homework 5: Web Caching PART 2: Functions and simulation Due Thursday Oct 9 at 11:55pm on bspace. About the data This homework is a continuation of the previous homework. We will be using the same websites data, Cache500. Load the data
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Course: Concepts In Computing With Data
Stat 133, Fall 2014 Homework 3: Data Frames, Plotting Due Thursday, Sept 25, by 11:55pm on bspace Directions: Turn in a plain text le containing the R commands you use to solve these problems and make these plots. Put your name in a comment at the top of
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Course: Introduction To Statistics
Stat 2 Fall 2014 Homework 10 1. Sixteen hundred draws will be taken from the following box True or false and explain: a) The expected value for the percentage of 1s from the box is exactly 75%. b) The expected value for the percentage of 1 for the percent
School: Berkeley
Course: Introduction To Statistics
Stat 2 Fall 2014 Homework 8 1. Election Day is coming up. Suppose that there are only two candidates in this race, Tweedle-Dum and Tweedle-Dee, and that Tweedle-Dum receives almost 50% of the total vote. An exit poll of voters is taken to try to predict t
School: Berkeley
Course: Introduction To Statistics
Stat 2 Fall 2014 Homework 1 1. A researcher examined published studies about a new treatment for patients with heart attacks. He found that if the study randomized patients between control and treatment groups, about 9% of patients in the treatment group
School: Berkeley
Course: Introduction To Statistics
Stat 2 Fall 2014 Homework #6 1. A class had two midterms. The average for midterm 1 was 70 with an SD of 10. The average for midterm 2 was 75 with and SD of 7. The correlation between the two was about 0.5. The scatter diagram was football shaped. a. What
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Course: Introduction To Statistics
Stat 2 Fall 2014 Homework 9 1. Election Day is coming up. Suppose that there are only two candidates in this race, Tweedle-Dum and Tweedle-Dee, and that Tweedle-Dum receives almost 50% of the total vote. An exit poll of voters is taken to try to predict t
School: Berkeley
Course: Introduction To Statistics
School: Berkeley
Course: Introduction To Statistics
Stat 2 Fall 2014 HW #3 1. For each of the following three sets of numbers, find the median, then find the average (show your work): a. 8 9 10 11 12 b. 8 9 10 11 100 c. 8 9 10 11 1000 Describe what you have discovered regarding averages and medians regardi
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Course: Introduction To Statistics
Stat 2 Fall 2014 Homework 10 1. Sixteen hundred draws will be taken from the following box True or false and explain: a) The expected value for the percentage of 1s from the box is exactly 75%. b) The expected value for the percentage of 1 for the percent
School: Berkeley
Course: Introduction To Statistics
Fall 2014 Stat 2 Homework #2 1. In searching for examples of histograms on the internet, I came across this page, which had the data given in the following table. From: http:/cribbd.com/learn/maths/data-handling/construct-and-interpret-a-histogram Distanc
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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
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