(Solved):
12. Let \( X \sim \operatorname{Gamma}(\alpha, \beta) \) where \( \alpha \) is an integer. Show th ...
12. Let \( X \sim \operatorname{Gamma}(\alpha, \beta) \) where \( \alpha \) is an integer. Show that for integers \( m \), \[ \mathrm{E}\left(X^{m}\right)=\frac{(m+\alpha-1) !}{(\alpha-1) ! \beta^{m}} \]