Thanks for answering

Let X1, X2, X3, . .. be independently random variables such that Xn ~Bin(n, 0.5) for n 2 1. Let N ~ Geo(0.5) and assume it is independent of X1, X2, .... Further define T = XN. (a) Find E(T) and argue that T is short proper. (b) Find the pof of T. (c) Use the pof of T in (b) to find P(T = n) for n 2 0. (d) Use the pof of T in (b) to find Var(T)