Suppose that X ~ B(12, p) and consider the point estimate
 = X/14
(a) What is the bias of this point estimate?
(b) What is the variance of this point estimate?
(c) Show that this point estimate has a mean square error of
3p - 2p2 / 49
(d) Show that this mean square error is smaller than the mean square error of X/12 when p ≤ 0.52.