Suppose X and Y are two independent and identically distributed geometric random rariables. The pmd of X is P(X = 1) = p(1 - p)*-1 for r = 1,2, ... Show that P(X 2) = (1– p)*-1. Show that P(X 2 *+T)|(X > T)] = P(X > x) where T is a positive integer, i.e., Find the moment-generating function of X. Let Z = X + Y. What is the moment generating function of Z?

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A: E(X−a)2=E(X−μ+μ−a)2=E((X−μ)+(μ−a))2=E((X−μ)2+2(X−μ)(μ−a)+(μ−a)2)=E(X−μ)2+E(2(X−μ)(μ−a))+E(μ−a)2=E(X−…

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A: Detailed solutions are given below.Explanation:X1 = 1,2,3,4,5 and X2 = 1,2,3,4,5,61) To find P(X1 =…