Let X1, X2, . . . , Xn denote a sample from a population whose mean value is unknown. Use the results of Example

Let X1, X2, . . . , Xn denote a sample from a population whose mean value θ is unknown. Use the results of Example 7.7b to argue that among all unbiased estimators of θ of the form

ni

=1 λiXi ,

ni

=1 λi = 1, the one with minimal mean square error has λi ≡ 1/n, i = 1, . . . , n.