Let X1, X2, , Xn denote a random sample from b(1, p) We know that x is an unbiased estimator of p and that Var(x) p(1 p) n (a) Find the RaoCramr lower bound for the variance of every unbiased estimator of p (b) What is the efficiency of X as an estimator of p ...

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Let X1, X2, . . . , Xn denote a random sample from b(1, p). We know

Question:

Let X1, X2, . . . , Xn denote a random sample from b(1, p). We know that x̄ is an unbiased estimator of p and that Var(x̄) = p(1 − p)/n.
(a) Find the Rao–Cramér lower bound for the variance of every unbiased estimator of p.
(b) What is the efficiency of X as an estimator of p?