2) Let {X}1 be a sequence of independent n=1 and identically distributed random variables with finite variance. Let = E(X1) and 02 = = .. Var(X1). Let Sh = X + + Xn and Xn = Sn/n. (a) Show that lim P(Xn ) = 1/2 n For the remainder of this question assume that, for each n, X, Poisson (1), i.e. is a Poisson random variable with parameter 1.