Let's denote the estimator as S = (n/(n-1))p(1-p). We want to find E(S), the expected value of S. First, we know that p = X/n, where X follows a binomial distribution with parameters n and . The expected value of X, E(X), is n. So, E(p) = E(X/n) = n/n = . The variance of X, Var(X), is n(1-). So, Var(p) = Var(X/n) = n(1-)/n = (1-)/n. Now, let's find E(S): E(S) = E[(n/(n-1))p(1-p)] = (n/(n-1))E[p - p] = (n/(n-1))[(E(p)) - E(p)] We already know that E(p) = . To find E(p), we use the formula