If Y has a binomial distribution with parameters n and p
a) Show that Y/n is an unbiased estimator of p.
b) To estimate the variance of Y, we generally use n(Y/n)(1-Y/n). Show that this estimator is a biased estimator of Var(Y).
c) Modify n(Y/n)(1-Y/n) to form an unbiased estimator of Var(Y).