Question: 12.3.6 Let X1 , . . . , X, be a random sample from a N(p, a2) distribution ( p and a2 are unknown), and

12.3.6 Let X1 , . . . , X, be a random sample from a N(p, a2) distribution ( p and a2 are unknown), and let 1 =(x-x) = (x - X) 72 1 2 n i=1 n

be two estimators of a2, (i) Compare the MSE's of S2 and ST. (ii) Consider n i=l as estimators of u2 and find k for which Sz has smallest MSE. Explain why, in practice, the only values of k used are (suboptimal): k = 1 and k = l/(n - 1).

1 =(x-x) = (x - X) 72 1 2 n i=1 n i=1

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