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 $\dfrac{\beta^2}{(\alpha-1)^2 (\alpha - 2)}$.
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 $\dfrac{\beta^2}{(\alpha-1)^2 (\alpha - 2)}$.