51. The mean square error of an estimator is MSE  . If is unbiased, then MSE  , but in general MSE  

(bias)2. Consider the estimator KS2, where S2

sample variance. What value of K minimizes the mean square error of this estimator when the sˆ

2 V1u ˆ 2 1u ˆ 2 V1u ˆ 2 1u ˆ 2 u ˆ

E1u ˆ  u22 1u ˆ 2 u ˆ

fY 1y2  •

nyn1 un 0 y

u 0 otherwise u ˆ

population distribution is normal? [Hint: Assuming normality, it can be shown that In general, it is dif cult to nd to minimize MSE , which is why we look only at unbiased estimators and minimize .]