In Problem 12(b), above, consider the alternative estimator \(t^{\star}(\mathbf{X})=S^{2}\) for estimating \(\theta^{2}\). In a mean square error sense, which estimator would you prefer for estimating \(\theta^{2}, t(\mathbf{X})\) or \(t^{\star}(\mathbf{X})\) ? Note \(\mu^{\prime}{ }_{r}=r ! \theta^{r}\) for an exponential PDF.