Problem 5. $X_1, X_2, \dots, X_n$ are iid $Gam(5, \lambda)$.
(a). Take $\hat{\lambda} = \frac{c}{\bar{X}}$. Find the constant $c$ to make $\hat{\lambda}$ an unbiased estimate of $\lambda$.
(b). Compute the MSE of the unbiased estimator $\hat{\lambda}$ in (a).
[hint: use the fact $\sum_{i=1}^n X_i \sim Gam(n\alpha, \lambda)$ if $X_1, \dots, X_n$ are iid $Gam(\alpha, \lambda)$].