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Each of the X, X,,.., X, are random variables with normal distribution N(m,o) and the correlation coefficient between the two pairs is equal to p. The random variable Y is also a binomial random variable B (n, p) independent of Xi. The sum of the random number of rand variables Xi is called S X, + X, +...+ Xy,Y = 1,2,..,n P, (k) = | k 1– p)"-* and a) Find the mean and the variance of S. b) Assuming that the X1, X2, ... are joint normal, if p=0 find the characteristic function of random variable S.

Each of the X, X,,.., X, are random variables with normal distribution N(m,o) and the correlation coefficient between the two pairs is equal to p. The random variable Y is also a binomial random variable B (n, p) independent of Xi. The sum of the random number of rand variables Xi is called S X, + X, +...+ Xy,Y = 1,2,..,n P, (k) = | k 1– p)"-* and a) Find the mean and the variance of S. b) Assuming that the X1, X2, ... are joint normal, if p=0 find the characteristic function of random variable S.

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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Each of the X, X,..., X, are random variables with normal distribution N(m,o) and the correlation coefficient between the two pairs is equal to p. The random variable Y is also a binomial random variable B (n, p) independent of Xi. The sum of the random number of rand variables Xi is called S X, +X, +...+ Xy,Y = 1,2,.,n P; (k) = k p*(1– p)*-k and a) Find the mean and the variance of S. b) Assuming that the X1 , X2, ... are joint normal, if p=0 find the characteristic function of random variable S.
Transcribed Image Text:Each of the X, X,..., X, are random variables with normal distribution N(m,o) and the correlation coefficient between the two pairs is equal to p. The random variable Y is also a binomial random variable B (n, p) independent of Xi. The sum of the random number of rand variables Xi is called S X, +X, +...+ Xy,Y = 1,2,.,n P; (k) = k p*(1– p)*-k and a) Find the mean and the variance of S. b) Assuming that the X1 , X2, ... are joint normal, if p=0 find the characteristic function of random variable S.
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