1.13

(a) Find two points 0 < p0 < p1 < 1 such that the estimator (1.11) for n = 1 is Bayes with respect to a distribution  for which P(p = p0) + P(p = p1) = 1.

(b) For n = 1, show that (1.11) is a minimax estimator of p even if it is known that po ≤ p ≤ p1.

(c) In (b), find the values p0 and p1 for which p1 − p0 is as small as possible.