Suppose that X1, , Xn form a random sample from the normal distribution with unknown mean and unknown variance 2 Let and be the two estimators of 2, which are defined as follows Show that the M S E of is smaller than the M S E of for all possible values of and 2 x 6 X, X ) and 61 i 1

Question: Suppose that X1, . . . , Xn form a random sample from the normal distribution with unknown mean and unknown variance 2. Let

Suppose that X1, . . . , Xn form a random sample from the normal distribution with unknown mean Î¼ and unknown variance Ïƒ2. Let and be the two estimators of Ïƒ2, which are defined as follows:

Show that the M.S.E. of is smaller than the M.S.E. of for all possible values of Î¼ and Ïƒ2.

x-. . 6 X,-X ) and 61 - i-1

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