Then kn is the usual unbiased estimator of p show that for

Question

For a given n ≥ 2, consider the family of binomial distributions, for the number K of successes in n independent trials with probability p of success on each trial. Thus any estimator (statistic) is a function of K = 0, 1,..., n. Then K/n is the usual unbiased estimator of p. Show that for n = 2 there is a unique unbiased estimator of p2. For what value(s) of K are its values remarkable?