3.16 Consider n binomial trials with success probability p, and letr and s be two positive integers with r + s

(a) Show that U is an unbiased estimator of zero if and only if U(k, n − k) = 0 for k = 0, 1,...,r −1 and k = n−s + 1, n−s + 2,...,n, and U(k, n−k) = ckU(r, s)

for k = r, . . . , n − s, where the c’s are given constants = 0.

(b) Show that δ is the UMVU estimator of its expectation if and only if

δ(k, n − k) = δ(r, s) for k = r, . . . , n − s.