Please see the attached file for full problem.
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 biasand variance of T_k as an estimator of sigma^2. Hene, or otherwise, find the value of k that minimizes the meansquared error of T_k as an estimator of sigma^2.
This solution helps with calculations involving unbiased estimators.