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### Lecture12_nofilm

Course: MATH 011, Fall 2009
School: UCSC
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through Continuity Continuity limits So the function sin(x) is continuous at x=0 Continuity through limits So the function f(x) is not continuous at x=0 Continuity limits So through the function f(x) is not continuous at x=3 Zooming in on a continuous function Zooming in on a continuous region Zooming in on a discontinuity

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UCSC - MATH - 011
Quizz 2: SequencesAttempt as many questions as you can. Write your nal answers on the dashed lines, and your working in the space provided. Partial credit will be given to correct reasoning.Question 1: [20 points] Find the next 2 terms in the seq
UCSC - MATH - 011
UCSC - MATH - 011
Quizz 4: Derivatives of basic functionsCalculators are not allowed. Attempt as many questions as you can. Write your answers on the dashed lines. Question 1: [70 points] Find the derivatives of the following functions with respect to the independen
UCSC - CMPE - 080
E-Commerce StandardsStandards, standards everywhere! Don't bother tracking the proposed e-commerce standards too closely right now-the landscape is changing on an almost a daily basis.Datamation June 1999EDI System ObstaclesData Company data ve
UCSC - AMS - 205
AMS 205 Homework 2due in class, Tuesday October 12 1. Let X1 and X2 have the joint pdf f (x1 , x2 ) = 15x2 x2 , 0 &lt; x1 &lt; x2 &lt; 1, zero elsewhere. Find 1 each marginal pdf and compute Pr(X1 + X2 1). Hint: Graph the space of X1 and X2 and carefully c
UCSC - AMS - 205
BASKIN SCHOOL OF ENGINEERING Department of Applied Mathematics and Statistics AMS 205 - Fall 2007Name:Midterm Please show your work in all the problems except for Problem 1. Problem 1: Specify which of the following statements are true and which
UCSC - AMS - 205
3.5 Let X = number of effective cases. If the new and old drugs are equally effective, then the probability that the new drug is effective on a case is .8. If the cases are independent then X binomial(100, .8), and100P (X 85) =x=85100 .8x .21
UCSC - AMS - 205
BASKIN SCHOOL OF ENGINEERING Department of Applied Mathematics and Statistics AMS 205 - Fall 2007Name:Quiz 1 Please show your work in all the problems. Problem 1: Let T &gt; 0 be a random variable with P r(T &gt; t) = aet + (1 a)et t &gt; 0, 0 &lt; 1 &lt; a, ,
UCSC - AMS - 205
AMS 205 Midterm Review Exercises1. You have a bowl of 20 cherries, of which 5 have pits and 15 have had their pits removed. Your cat knocks over the bowl and 4 cherries fall on the oor and are eaten (including any pits) by your dog. You pick up one
UCSC - AMS - 205
AMS 205 Homework 4due in class, Tuesday October 26 1. Let X be the mean of a random sample of size 5 from a normal distribution with = 0 and 2 = 125. Determine c so that P (X &lt; c) = 0.90. 2. Let X1 , . . . , X25 and Y1 , . . . , Y25 be two indepe
UCSC - AMS - 205
AMS 205 Homework 6due in class, Tuesday November 16 1. Let X1 , . . . , Xn be a random sample from each of the distributions having the following probability density functions: (a) f (x; ) = x(1) , 0 &lt; x &lt; 1, 0 &lt; &lt; , zero elsewhere (b) f (x; ) =1
UCSC - AMS - 205
AMS 205 Homework 9optional problems, not to be turned in the rst two are likelihood ratio test problems, which is a topic for the nal exam the second two are from chapter 8, which will not be on the nal 1. Let X1 , . . . , Xn be a random sample fro
UCSC - AMS - 205
AMS 205 Homework 5due in class, Tuesday November 9 1. Compute an approximate probability that the mean of a random sample of size 15 from a distribution having pdf f (x) = 3x2 , 0 &lt; x &lt; 1, zero elsewhere, is between 3/5 and 4/5. 2. We know that X i
UCSC - AMS - 205
UCSC - AMS - 205
AMS 205 - HomeworkChapter 2 - Transformations and Expectations Solutions2.1 a. fx (x) = 42x5 (1 x), 0 &lt; x &lt; 1; y = x3 = g(x), monotone, and = (0, 1). Use Theorem 2.1.5. fY (y) = fx (g 1 (y) d 1 d 1 g (y) = fx (y 1/3 ) (y 1/3 ) = 42y 5/3 (1 y 1/3
UCSC - AMS - 205
BASKIN SCHOOL OF ENGINEERING Department of Applied Mathematics and Statistics AMS 205 - Fall 2006Name:Final Please show your work in all the problems except for Problem 1. Problem 1: Specify which of the following statements are true and which ar
UCSC - AMS - 205
BASKIN SCHOOL OF ENGINEERING Department of Applied Mathematics and Statistics AMS 205 - Fall 2007Name:Quiz 2 Please show your work in all the problems. Problem 1: Let X be a random variable with a Student t distribution with p degrees of freedom.
UCSC - AMS - 205
AMS 205 - HomeworkChapter 7 - Point Estimation Solutions7.6 a. f (x|) = Theorem. b. L(|x)n (-2 i xi )I,) (x(1) ). i xi -2I,) (x(1) ).This x(1) is a sufficient statistics for by the Factorizationn is increasing in . The second term does not in
UCSC - AMS - 205
UCSC - AMS - 205
UCSC - AMS - 205
AMS 205 Homework 3due in class, Tuesday October 19 1. Let X1 , X2 , and X3 be independent RVs, each with pdf f (x) = exp(x)I {0&lt;x&lt;} . Find the distribution of Y = minimum(X1 , X2 , X3 ). Hint: P r(Y y) = 1 P r(Y &gt; y) = 1 P r(X1 &gt; y, X2 &gt; y, X3 &gt;
UCSC - AMS - 205
UCSC - AMS - 205
AMS 205 Homework 7due in class, Tuesday November 23 1. Let us assume that the life of a tire in miles, say X, is normally distributed with mean and standard deviation 5000. Past experience indicates that = 30, 000. The manufacturer claims that th
UCSC - AMS - 205
UCSC - AMS - 205
UCSC - AMS - 205
UCSC - AMS - 205
UCSC - CMPS - 012
Write a class to represent time on a 24 hour clock, to the nearest minute. The Time values (objects) should be mutable (like StringBuffer). Provide an operation to add minutes or hours to a Time value changing the object. Also provide an operation to
UCSC - CMPS - 012
Program warm-up for the day.Write a METHOD that takes two parameters, a int for the length of a line, and a char for the character to use to draw the line. The method prints length characters. Use the method in a program to draw a triangle like the
UCSC - CMPS - 012
Write a class to represent rectangles. The class should have a constructor, and methods toString(), getArea(), getPerimeter(), and draw(). The class should work with the test program RectangleTest (see other screen) producing the following output for
UCSC - CMPS - 012
class QueryTest { static final int YES = 1, NO = 2; static final int RIGHT = 1, LEFT = 2; public static void main(String[] args) { Query continueQuery = new Query(&quot;Do you want to continue? (yes or no)&quot;, &quot;yes&quot;, &quot;no&quot;); Query rightOrLeft = new Query(&quot;Sh
UCSC - CMPS - 012
Program warm-up for the day.Write a program that asks for one integer, the height of a right triangle, and then draws a triangle of that size using asterisks. E.g. for input 4 that would be:* * * *Bonus feature: draw only the outline of the trian
UCSC - CMPS - 012
Write a method to read in a Sentence and return it given a single parameter of type Scanner. Use that method to read in a Pattern and return it given a single parameter of type Scanner.Program warm-up for the day.
UCSC - CMPS - 012
Program warm-up for the day.Write a program that prompts for the length of three line segments as integers. If the three lines could form a triangle, the program prints &quot;Is a triangle.&quot; Otherwise it prints &quot;Is not a triangle.&quot; Recall that the sum of
UCSC - CMPS - 012
Why functions (methods)? Reduce redundant code - If you use it twice, make it a function Simplify main programs/procedures Provide abstraction/decomposition/interfaces Building blocks - make new statements Recursion Object oriented and top down
UCSC - CMPS - 012
Statements and Control Flow The programs we have seen so far do exactly the same list of instructions every time What if we want to do different things for different inputs? Do some action only if a specified condition is met We need conditional
UCSC - CMPS - 012
What is a Program? (part 1) A recipe for doing something A precise set of instructions Like the rules for a game, or how to build something, or directions to your house Tic-Tac-ToeDraw a big # First player draws an X in a square Second playe
UCSC - CMPS - 012
Arrays (ch 5) concepts memory (heap) kinds of locals (references) syntax: [] keyword: new power!Arrays Only single data items so far What if you want to handle many related data items of the same type? An array is a container that holds a
UCSC - CMPS - 012
Quiz 3 Results 20 Points possible Max: Min: Mean: Median:Chapter 5: Arrays We have seen how to declare array:int[] quizScore; - declares an array of ints double[] temperature; - declares an array of doubles String[] lastName; - declares an a
UCSC - CMPS - 012
Scope: Local Variables We have discussed the scope of local variables (ones defined in methods) alreadyA variable's scope extends from the line it is declared until the end of the block it is contained in A formal parameter's scope is the entire me
UCSC - CMPS - 012
Announcements TA Office Hours Sanjit Jhala Tuesday 4 5, BE 352Chapter 3 Statements and Control Flow Up to now, all of our programs have executed from top to bottom without making any decisions These programs do exactly the same thing every t
UCSC - CMPS - 012
Extra Credit Assignment Posted on homework section of web site Due February 24 You must send me email by Friday, Feb 7 if you are going to work on this assignment Everything that you need to know should be on the web site Let me know if you have
UCSC - AMS - 005
Name: AMS-5: Statistics Quiz 2 (Tuesday October 17, 2006)Section:Quizzes are closed-book, closed-notes, with the exception of one (letter size) piece of paper with formulas on both sides. Please show all your work. Good luck! (Hypothetical.) A ne
UCSC - AMS - 007
AMS 7LLAB #3 Probability and Discrete DistributionsFall, 2007Objectives: 1. To explore relative frequency and the Law of Large Numbers 2. To practice the basic rules of probability 3. To work with the binomial and Poisson distributions in JMP G
UCSC - AMS - 007
University of California Department of Applied Mathematics and Statistics Baskin School of Engineering Winter 2003Engineering 7: Biostatistics Lectures: Tu-Th 4-5.45pm, in Steven Acad 150. Instructor: Raquel Prado, Baskin Engineering 149; 459-148
UCSC - AMS - 007
AMS 7LLAB #7 Hypothesis TestingFall, 2007Objectives: 1. To practice the 6-step method for hypothesis testing 2. To practice using JMP to perform hypothesis tests 3. To practice interpreting JMP output and drawing conclusions Getting Started: Lo
UCSC - AMS - 007
AMS 7LLAB #4 The Central Limit TheoremFall, 2007Objectives: 1. To practice with the normal distribution 2. To explore the Central Limit Theorem Getting Started: Log onto your machine and start JMP. There are no datasets to download for today. P
UCSC - AMS - 007
AMS 7LLAB #9 Goodness-of-Fit, Regression, and ANOVAFall, 2007Objectives: 1. To practice goodness-of-t tests 2. To practice using JMP for multiple regression analysis and Analysis of Variance Getting Started: There are two les to download today.
UCSC - AMS - 007
AMS 7LLAB #1 Data Types and Introduction to JMPFall, 2007Objectives: 1. To introduce the use of the statistical software package JMP 2. To review data type classications 3. To practice basic data display methods Getting Started: Log onto your m
UCSC - AMS - 007
WINTER03, ENG-7RAQUEL PRADO AMS, UC Santa Cruz1StatisticsThe Oxford Dictionary: n.pl. 1 (usu. sing.) science of collecting and analyzing signicant numerical data. 2 such analyzed data. Pagano &amp; Gauvreau: the study of statistics explores the co
UCSC - AMS - 007
ENG-7: BiostatisticsENG-7: BiostatisticsScatterplots In the example we have x = 63 and y = 152. x200y 136 198 194 140 93 172 116 174 145 Sum(xi - x) -3 6 3 1 -9 4 -4 2 0 0(yi - y ) -16 46 42 -12 -59 20 -36 22 -7 0(xi - x)2 9 36 9 1
UCSC - AMS - 007
AMS 7LLAB #5 Mid-Quarter ReviewFall, 2007Objectives: 1. To review concepts from the rst half of the course 2. To practice with condence intervals Getting Started: Log onto your machine and download the cereal.txt datale from the class webpage:
UCSC - AMS - 007
t 4 q3 # } s ) )' ' v '3 # #'3 # 6 4 1 )' % # t 6 #q ' t 4' ' lBs&amp;xi&amp;' &amp;t(# 0dDgi&amp;205&amp;530&amp;(bB'&amp;5gtwe)ze'tgt5 1&amp; i&amp;0B'no@l0@(5@Bqi&amp;53iB'tr&amp;5tw(w5ieqtt5o(H5ti5xf 4 q# t f s' '%q #'3# 6 4 1 t 6#q ' 14 6#3 4 ' # ' 6 qq t lBs&amp;4
UCSC - AMS - 007
Discussion # 2 1. (Rosner, page 67) Estimates of the prevalence of Alzheimer's disease (cases per 100 population) are given in the following table, Age Males Females 65-69 1.6 0.0 70-74 0.0 2.2 75-79 4.9 2.3 80-84 8.6 7.8 85+ 35.0 27.9 Suppose an unr
UCSC - AMS - 007
AMS 7LLAB #6 Condence IntervalsFall, 2007Objectives: 1. To explore condence intervals via simulation 2. To practice computing condence intervals Getting Started: Log onto your machine and start JMP. There are no datasets to download for today.
UCSC - AMS - 007
AMS 7LLAB #2 Exploratory Data AnalysisFall, 2007Objectives: 1. To practice exploratory data analysis techniques 2. To learn to read datafiles into JMP Getting Started: Log onto your machine using your ITS login. Before starting JMP, you need to
UCSC - AMS - 007
AMS 7LLAB #8 Linear RegressionFall, 2007Objectives: 1. To practice using JMP to perform linear regression 2. To practice interpreting JMP output and drawing conclusions Getting Started: There are two les to download today. Log onto your machine
UCSC - AMS - 007
Discussion 1. Problem 9.5, page 227. In addition to parts (a)-(e) construct a one-sided 95% condence interval lower bound for d . 2. Problem 9.8, page 228. In addition to parts (a)-(d), construct one-sided 90% condence intervals upper bound for 1
UCSC - AMS - 007
Discussion # 4. (Probability Distributions) 1. An experiment is conducted to test the effect of an anticoagulant drug on rats. A random sample of 4 rats is employed in the experiment. If the drug manufacturer claims that 80% of the rats will be favor
UCSC - AMS - 007
Raquel Prado Applied Mathematics and Statistics ENG-7. Winter 2003Quiz 1Name:1. A study was conducted to determine urine flow of sheep (in millimeters/minute) when infused intravenously with the antidiuretic hormone ADH. The urine flows of 6 she
UCSC - AMS - 007
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