Question: Let X, X.X, be a random sample from a population with mean and variance o. Also, let C. C. c. be any set of fixed

Let X, X.X, be a random sample from a population with mean and variance o. Also, let C. C.

c. be any set of fixed numbers, and consider the estimator of p

(a) Show that is an unbiased estimator of if and only if

(b) Show that the variance of is Var (A) (c++...+

(c) Show that if is an unbiased estimator of --'+n' Note that, if we are free to choose the numbers

c, this expression is minimized by setting for

(d) Using the results in

(a) (c), show that of all estimators of the form A. the sample mean is the most efficient.

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