An estimate of population proportion is p-hat (henceforth p), where p=(x/n), where x is a binomial, Bin(n,p).

The variance of p-hat is estimated by [p(1-p)]/n = (1/n)[p(1-p)] = (1/n)(x/n)[1-(x/n)].

Is this an unbiased estimator of the actual variance of p?

A given hint suggests "Use the fact that Var(x)=E(x^2)-E(x)^2"