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

QUESTION:

Let \(X_{1}, X_{2}, \ldots, X_{n}\) denote a random sample from \(b(1, p)\). We know that \(\bar{X}\) is an unbiased estimator of \(p\) and that \(\operatorname{Var}(\bar{X})=p(1-p) / n\). (See Exercise 6.4-12.)

(a) Find the Rao-Cramér lower bound for the variance of every unbiased estimator of $p$.

(b) What is the efficiency of \(\bar{X}\) as an estimator of \(p\)?

Equation Transcription:

Text Transcription:

X_1,X_2,…,X_n  

b(1,p)  

Bar X  

p  

Var bar⁡(X)=p(1-p)/n