Let the random variables X1, X2,... be independent and identically distributed (i.i.d). Suppose N is a nonnegative, inte

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Let The Random Variables X1 X2 Be Independent And Identically Distributed I I D Suppose N Is A Nonnegative Inte 1 (55.21 KiB) Viewed 109 times

Let the random variables X1, X2,... be independent and identically distributed (i.i.d). Suppose N is a nonnegative, integer-valued random variable that is independent of X1, X2, X3..... Denote the random variable Z as follows: N z = Xi Let Xi's be i.i.d. Ge(0.2)-distributed, and N be Ge(0.8)-distributed. (a) [6 points] Find the probability mass function of 2. (b) [6 points] Compute Cov(32,N +Z). Your result can be expressed using expectations and variances of Xi and N. (c) [8 points] Show that Z|Z >O E Fs(a), and determine the value of a.