3. There are two competing estimators for $\sigma^{2}$ : $$ What{\sigma)_{\mathrm{MLB} }^{2}=\frac{1}{n} \sum_{i=1}^{n}\left(X_{i}-\bar{X} ight)^{2} \quad \text { vs } \quad S^{2}=\frac{1}{n-1} \sum_{i=1}^{n}\left(X_{i}- \bar{X} ight)^{2}=\frac{n}{n-1} That{\sigma)_{\mathrm{MLE}}^{2} . $$ (a) ( 3 pts) Find their expected values. Are they unbiased? (b) (3 pts) Find their variances. (c) (3 pts) Find the relative efficiency of the two estimators, i.e., eff $\left(\hat{\sigma)^{2}, S^{2} ight) $. Which estimator is better in terms of MSE? What if $n ightarrow \infty$ ? S.P.PB. 370