1. Suppose that X1,.... Xn are independent and identically distributed Poisson(A) ran- dom variables with probability function f(z; A) = r = 0, 1,2. . .. Define X and S as X =_) X; and =_ i=1 i=1 (a) Find E(X ) and Var(X). (b) Show that X 4 1. (c) Show that E(S) = A(X + 1). (d) Let D = S - X. Show that D is an unbiased estimator of A?. (e) If A = 1 use the Central Limit Theorem to find an approximation for P(X,+ X2 + . .. + X100