Calculations with unbiased estimators
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a) Using the results for the gamma distribution, show that s^2 is an unbiased estimator of sigma^2. Also state its variance.
b) Consider a statistic of the form T_k = ks^2, for some constant k. Find expressions for the bias and variance of T_k as an estimator of sigma^2. Hene, or otherwise, find the value of k that minimizes the mean squared error of T_k as an estimator of sigma^2.
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