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.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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