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Let 5'2 be the sample variance of a random sample drawn from a N (,u, 02) distribution. Show that the constant c = (n 1)

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Let 5'2 be the sample variance of a random sample drawn from a N (,u, 02) distribution. Show that the constant c = (n 1) / (n + 1) minimizes E[(c.5'2 02m. Hence, the estimator (n + 1)'1 221:1(Xi X)2 of 02 minimizes the mean square error among estimators of the form (:82. [10 marks]

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