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For $X$ a gamma random variable with parameters $\alpha >2$ and $\beta> 0$

a) Prove that the mean of $\dfrac1X$ is $\dfrac{\beta}{\alpha-1}$.

b) Prove that the variance of $\dfrac1X$ is $\dfrac{\beta^2}{(\alpha-1)^2 (\alpha - 2)}$.

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    What did you try? Can you write a density? Which integral do have to compute?2012-09-13

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