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6.52 Let Y and Y2 be independent Poisson random variables with means 2, and A2, respectively. Find the a probability function of Y, + Y2. b conditional probability function of Y1, given that Y, + Y2 = m.

6.52 Let Y and Y2 be independent Poisson random variables with means 2, and A2, respectively. Find the a probability function of Y, + Y2. b conditional probability function of Y1, given that Y, + Y2 = m.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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I need help with problem 6.52 in the photo.
pter 6 Functions of Random Variables the north-south distance between the landing point and the target center and let Y2 denote the corresponding east-west distance. (Assume that north and east define positive directions ) The distance between the landing point and the target center is then U = are independent, standard normal random variables, find the probability density function for U VY} + Y}. If Y, and Y; Let Y be a binomial random variable with n¡ trials and probability of success given by p. Let Y, be another binomial random variable with n2 trials and probability of success also given by p. If Y, and Y2 are independent, find the probability function of Y1 + Y2. 6.49 Let Y be a binomial random variable with n trials and probability of success given by p. Show that n- Y is a binomial random variable with n trials and probability of success given by 1 – p. 6.50 6.51 Let Y be a binomial random variable with n, trials and p = .2 and Y, be an independent bino- mial random variable with n2 trials and p2 = .8. Find the probability function of Y¡ +n2 – Yp. 6.52 Let Y and Y2 be independent Poisson random variables with means 21 and 22, respectively. Find the a probability function of Y, + Y2. b conditional probability function of Y1, given that Y, + Y2 = m. 6.53 of Let Y1, Y2, . .. , Y, be independent binomial random variable with success given by pi, i = 1, 2, . . , n. trials and probability If all of the n; 's are equal and all of the p's are equal, find the distribution of >i=1. b If all of the n;'s are different and all of the p's are equal, find the distribution of Li=l* c If all of the n¡'s are different and all of the p's are egual, find the conditional distribution Yi given E=1 Y; = m. d If all of the n¡'s are different and all of the p's are equal, find the conditional distribution Y,+ Y2 given =1 Yi = m. e If all of the p's are different, does the method of moment-generating functions work wer to find the distribution of - Y;? Why? a i=1 6.54 Let Y, Y2, ... , Y, be independent Poisson random variables with means respectively. Find the a probability function of "
Transcribed Image Text:pter 6 Functions of Random Variables the north-south distance between the landing point and the target center and let Y2 denote the corresponding east-west distance. (Assume that north and east define positive directions ) The distance between the landing point and the target center is then U = are independent, standard normal random variables, find the probability density function for U VY} + Y}. If Y, and Y; Let Y be a binomial random variable with n¡ trials and probability of success given by p. Let Y, be another binomial random variable with n2 trials and probability of success also given by p. If Y, and Y2 are independent, find the probability function of Y1 + Y2. 6.49 Let Y be a binomial random variable with n trials and probability of success given by p. Show that n- Y is a binomial random variable with n trials and probability of success given by 1 – p. 6.50 6.51 Let Y be a binomial random variable with n, trials and p = .2 and Y, be an independent bino- mial random variable with n2 trials and p2 = .8. Find the probability function of Y¡ +n2 – Yp. 6.52 Let Y and Y2 be independent Poisson random variables with means 21 and 22, respectively. Find the a probability function of Y, + Y2. b conditional probability function of Y1, given that Y, + Y2 = m. 6.53 of Let Y1, Y2, . .. , Y, be independent binomial random variable with success given by pi, i = 1, 2, . . , n. trials and probability If all of the n; 's are equal and all of the p's are equal, find the distribution of >i=1. b If all of the n;'s are different and all of the p's are equal, find the distribution of Li=l* c If all of the n¡'s are different and all of the p's are egual, find the conditional distribution Yi given E=1 Y; = m. d If all of the n¡'s are different and all of the p's are equal, find the conditional distribution Y,+ Y2 given =1 Yi = m. e If all of the p's are different, does the method of moment-generating functions work wer to find the distribution of - Y;? Why? a i=1 6.54 Let Y, Y2, ... , Y, be independent Poisson random variables with means respectively. Find the a probability function of "
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