Let $X_{1}, \ldots, X_{n}$ be a random sample of size n from the gamma distribution $\operatorname{gamma) (\alpha, \beta) $, with $\alpha$ known. Prove that $\hat{\beta)=\frac{1}{n \alpha} \sum_{i=1}^{n} X_{i}$ is the best unbiased estimator of $\beta$. SP.DL.2271