Let 123 , , ,..., XXX Xn be a sequence of independent and identically distributed discrete random variables, each with probability mass function

P(X=k) = e^-aa^k/k! for k=0,1,2,3....

Define sample mean as X(with bar)=1/n?X_i. i=1 (a) Find the expected value and the variance of X (with bar). (b) Find the probability mass function of .X (with bar) (c) Find an approximate pdf of X (with a bar) when n is very large (n??).