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


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Given that X ~ Gamma(?,?) wh
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