Inferential Statistics Theory of Estimators

Let X ~ BIN (n,p) and = X/n.

(a) Find a constant c so that E[c()(1-)] = p(1-p).

(b) Find an unbiased estimator of Var (X).

(c) Consider a random sample of size N from BIN (n,p). Find unbiased estimators of p and Var (X) based on the random sample.