Suppose that Xi, i = 1,..., n, are iid Bernoulli(p). (a) Show that the variance of the

Question:

Suppose that Xi, i = 1,..., n, are iid Bernoulli(p).
(a) Show that the variance of the MLE of p attains the Cramer-Rao Lower Bound.
(b) For n ≥ 4, show that the product X1X2X3X4 is an unbiased estimator of p4, and use this fact to find the best unbiased estimator of p4.