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4. Consider A Normal Population With Variance O?. (a) Consider The Family Of Estimators Yo For O?, W

4. Consider a Normal population with variance o?. (a) Consider the family of estimators Yo for o?, where Yo = 1 LX (Xi – X)2 and b is a positive constant. Note that Yn-1 = S2 and thus the sample variance is a member of this family of estimators. Find an expression (simplified as much as possible) for MSE(Y), note that your answer will depend on b. (Hint: It might be useful to write Y, in terms of S2 and use what you know about S2 in the case of Normal Populations). (b) Suppose b* is the value of b which minimizes MSE (Y). Find an expression for b*. (c) Is You an unbiased estimator of o?, an asymptotically unbiased estimator of o?, or neither? (d) For any given sample, what can you say about the relative sizes of Yb* and s? What happens when n + ?