Let X have the gamma distribution with parameters 2 and 0 a Prove that the mean of 1 X is ( 1) b Prove that the variance of 1 X is 2 ( 1)2 ( 2)

Question: Let X have the gamma distribution with parameters > 2 and > 0. a. Prove that the mean of 1/X is /(

Let X have the gamma with parameters α > 2 and β > 0.
a. Prove that the mean of 1/X is β/(α − 1).
b. Prove that the variance of 1/X is β2/[(α − 1)2 (α − 2)].

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