Question: Let X have a binomial(n, ) distribution. Then Y = X/n is an unbiased estimator of . However, the variance of Y , ( 1

Let X have a binomial(n, ) distribution. Then Y = X/n is an unbiased estimator of . However, the variance of Y , (1)/n , depends upon and this can cause difficulties when we need to apply a statistical method that requires the variance to be independent of . Using the equation

Var(f(Y)) = [f'(E|Y])]^2Var(Y) find a transformation f of Y that makes Var[f(Y)] independent of

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