If X1,...,XN are iid Binomial (n,p ) random variables, find the UMVUE of theta = pn = P(X1 = n). Solution complete sufficient statistic for p is sum(X_i) and indicator {X_1=n} is an unbiased estimator of p. Hence expectation of indicator of X_1=n given sum(X_i) is UMVUE of p^n..