Problem 7.43 Let X1,...,Xn be a random sample from a Bernoulli distribution. Show that E(p(1 p)) = n 1 n p(1

Problem 7.43 Let X1,...,Xn be a random sample from a Bernoulli distribution. Show that E(ˆp(1 − pˆ)) = n − 1 n × p(1 − p) < p(1 − p). Deduce that pˆ(1 − pˆ) is a biased estimator of p(1 − p).