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3 Pages

### hw5solns

Course: STA 4321, Spring 2010
School: University of Florida
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Word Count: 453

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to Solutions Homework 5 4.45 Let X denote the number of underfilled cartons in the selected 50 cartons, If 50 cartons are selected independently, then X can be modeled to have a binomial distribution with p . a. p = 0.05, We then have 2 P ( X 2) = p ( x) x =0 2 50 = (0.05) x (1 0.05)50 x x =0 x = 0.5405 b. p = 0.1, We then have 2 P ( X 2) = p ( x ) x =0 2 50 = (0.1) x (1 0.1)50 x x=0 x =...

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to Solutions Homework 5 4.45 Let X denote the number of underfilled cartons in the selected 50 cartons, If 50 cartons are selected independently, then X can be modeled to have a binomial distribution with p . a. p = 0.05, We then have 2 P ( X 2) = p ( x) x =0 2 50 = (0.05) x (1 0.05)50 x x =0 x = 0.5405 b. p = 0.1, We then have 2 P ( X 2) = p ( x ) x =0 2 50 = (0.1) x (1 0.1)50 x x=0 x = 0.1117 4.49 a. The assumption is that every inspection is an independent event. b. P (a wing crack is detected) = p1 p2 p3 = 0.36 Let X denote the number of planes detected a wing crack, the binomial distribution is a reasonable model for this experiment, p = 0.36 , then P ( X 1) = 1 P ( X = 0) 3 0 3 = 1 ( 0.36 ) ( 1 0.36 ) 0 = 0.7379 4.54 Let X denote the number of components last longer than 1000 hours, then X can be modeled to have a binomial distribution with p = 1 0.15 = 0.85 a. We have 4 P ( X = 2) = (0.85) 2 (1 0.85) 2 = 0.0975 2 b. If the subsystem operates for longer than 1000 hours, any two or more of the four components last for more than 1000 hours, so we get 4 4 4 P ( X 2) = (0.85) 2 (1 0.85) 2 + (0.85)3 (1 0.85)1 + (0.85) 4 (1 0.85) 0 2 3 4 = 0.988 4.58 a. X has a binomial distribution with p = 0.1 n 0 P ( X 1) 1 = P ( X = 0) = 1 ( 0.1) (1 0.1) n = 1 0.9n = 0.95 0 Thus n = log 0.05 = 28 log 0.9 b. X has a binomial distribution with p = 0.1 n 0 n P ( X 1) = 1 P ( X = 0) = 1 ( 0.05 ) ( 1 0.05 ) = 1 0.95n = 0.95 0 Thus n = log 0.05 = 58 log 0.95 4.60 For each case, 3 3 x 3 x P(innocent people receiving death penalty) = 0.01 ( 0.05 ) ( 1 0.05 ) x =2 x = 0.0000725 Let X denote the number of innocent people receiving death penalty, X can be modeled as a binomial distribution with n = 100, p = 0.0000725 , then E ( X ) = np = 100 0.0000725 = 0.00725 V ( X ) = np ( 1 p ) = 100 0.0000725 0.9999275 = 0.007249 = V ( X ) = 0.0851 4.67 Let X denote the number of defective engines tested before a good engine is found, X can be modeled as a geometric distribution with p = 1 0.1 = 0.9 , we need to calculate P ( X = 2) P ( X = 2) = q 2 p = ( 0.1) 0.9 = 0.009 2 4.68 Define event A: the first two engines are defective event B: at least four defective engines are tested before the first nondefective engine is found. We need to find P ( B | A) = P ( B A) P ( A) The first and second test are independent, then we have P ( A) = 0.1 0.1 = 0.01 Event B A , then P ( B A) = P ( B ) = (0.1) k 0.9 = 0.0001 k =4 Therefore, P ( B | A) = 0.0001 = 0.01 0.01
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University of Florida - STA - 4321
Solutions to Homework 64.78Let Y be the number of people who refuse to be interviewed before she obtains fivepeople, soY = X 5, Y can reasonably be assumed to have the negative binomial distributionwith p = 0.6 , r = 5a.P ( X 7) = P (Y 2)2i + 45
University of Florida - STA - 4321
Solutions to Homework 75.5a. 00f x dx ce x /10 dx 10 ce x /10thus c 10c 11.10b. if b 0, F (b) 0 , if b 0, thenF (b) bf ( x)dx b0b1 x /10edx e x /10 1 e b /10010thus1 e b /10 ,F (b) 0,b0b0c. P( X 15) 1 P( X 15) 1 P( X 15) 1 (
University of Florida - STA - 4321
Solutions to Homework 85.27ba. P( X c) c1bcdx bababdP X d b a b db. P X d | X c P X c b c b cba5.39Let X denote the travel distances, it is uniformly distributed between points a and b .aba. P X 2aba2 0.5baa 3b a 3b b. P X a 3
University of Florida - STA - 4321
Solutions to Homework 95.85Let X denote the amount spent for maintenance and repairs in a certain company inthe next week, then X has an approximately normal distribution with mean of 600 andstandard deviation of 40. Hence, the probability that actual
University of Florida - STA - 4321
University of Florida - STA - 4321
Solutions to Homework 116.23For a fixed Y y [0,1] , we have 0 x 1 y , then the marginal pdf of Y isfY ( y ) f ( x, y )dx1 y 2dx0 2(1 y ),0 y 1Then, the conditional probability density function for X given Y y isf X |Y ( x | y 0.25) f X ,Y ( x,
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
STA 4321/5325 - Spring 2010Quiz 1 - January 22, 2010Name:All problems have exactly one correct answer.Problem 1 Consider an experiment which consists of tossing a fair coin 1000 times. The totalnumber of possible outcomes for the complete experiment
University of Florida - STA - 4321
STA 4321/5325 - Spring 2010Quiz 2 - January 29Name:There are ve problems in this quiz. Each problem has exactly one correct answer.Problem 1 The probability that Traver eats breakfast and gets to work on time is 0.2. Theprobability that he eats break
University of Florida - STA - 4321
STA 4321/5325 - Spring 2010Quiz 3 - February 12Name:There are ve problems in this quiz. Each problem has exactly one correct answer.Problem 1 Let us recollect that R represents the set of real numbers and S represents the samplespace of a random expe
University of Florida - STA - 4321
STA 4321/5325 - Spring 2010Quiz 4 - February 19Name:There are ve problems in this quiz. Each problem has exactly one correct answer.Problem 1 A Bernoulli experiment has(a) 1 outcome(b) 2 outcomes(c) 3 outcomes(d) 4 outcomesProblem 2 If X is a bin
University of Florida - STA - 4321
STA 4321/5325 - Spring 2010Quiz 5 - March 19Name:There are ve problems in this quiz. Each problem has exactly one correct answer.Problem 1 Let X be a continuous random variable which takes non-negative values. Let f (x)denote the probability density
University of Florida - STA - 4321
STA 4321/5325 - Spring 2010Quiz 6 - March 26Name:There are ve problems in this quiz. Each problem has exactly one correct answer.Problem 1 Let f (x) denote the probability density function of a gamma random variable withparameters and .f (x) =Then
University of Florida - STA - 4321
STA 4321/5325 - Spring 2010Quiz 7 - April 2Name:There are ve problems in this quiz. Each problem has exactly one correct answer.Problem 1 The moment-generating function of a continuous random variable X with aprobability density function f (x) is giv
University of Florida - STA - 4321
STA 4321/5325 - Spring 2010Quiz 8 - April 9Name:There are ve problems in this quiz. Each problem has exactly one correct answer.Problem 1 Let f (x, y ) denote the joint probability density function of two continuous randomvariables X and Y , and fX (
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - STA - 4321
STA 4321/5325 - Spring 2010Sample Exam 2Note: This is an example adapted from previous STA 4321/5325 exams. It is intended to be ofapproximately the same length and style as the actual exam. However, it is NOT guaranteed tomatch the content or coverag
University of Florida - STA - 4321
STA 4321/5325 - Spring 2010Sample Exam 2Note: This is an example adapted from previous STA 4321/5325 exams. It is intended to be ofapproximately the same length and style as the actual exam. However, it is NOT guaranteed tomatch the content or coverag
University of Florida - STA - 4321
STA 4321/5325 - Spring 2010Sample Exam 3Note: This is an example adapted from previous STA 4321/5325 exams. It is intended to be ofapproximately the same length and style as the actual exam. However, it is NOT guaranteed tomatch the content or coverag
University of Florida - STA - 4321
STA 4321/5325 - Spring 2010Sample Exam 3Note: This is an example adapted from previous STA 4321/5325 exams. It is intended to be ofapproximately the same length and style as the actual exam. However, it is NOT guaranteed tomatch the content or coverag
University of Florida - STA - 4321
STA 4321/5325 - Spring 2010Sample Exam 4Note: This is an example adapted from previous STA 4321/5325 exams. It is intended to be ofapproximately the same length and style as the actual exam. However, it is NOT guaranteed tomatch the content or coverag
University of Florida - STA - 4321
STA 4321/5325 - Spring 2010Sample Exam 4Note: This is an example adapted from previous STA 4321/5325 exams. It is intended to be ofapproximately the same length and style as the actual exam. However, it is NOT guaranteed tomatch the content or coverag
University of Florida - STA - 4321
University of Florida - STA - 4321
University of Florida - MAR - 3503
Consumer BehaviorMAR 3503Fall 2010Questions for review, Exam 1These questions should help you organize your thoughts and prepare for the exam. The sequestions are, in general, much broader than the questions youll find on the exam; that meansthat th
University of Florida - MAR - 3503
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University of Florida - MAR - 3503
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University of Florida - MAR - 3503
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University of Florida - MAR - 3503
Consumer BehaviorMAR 3503, Sections 0111, 2948, and 2950Fall 2010Individual Written AssignmentDue at the start of class, Wednesday, September 15Worth: 20 pointsFor this assignment, you will design research strategies to compare how well two advertis