a) Prove that for any constant Q, (X-X)Q=0 i=1 b) Use (a) to prove, N N (X-X)(Yi-Y) = (X-X)Yi i=1 i=1 c) Prove that E(X) = x. d) Prove that Var (X) = 0/N for iid X. What happens as N o? e) Suppose that X, X2,..., Xy is an iid sample of data. Prove the following is an unbiased estimator for the variance, : N 1 N-1 (x x)2