Be certain that you understand every step in this derivation (refer to Eq. (3.55) and to the equation just below it if you are uncertain).

Use the same procedure to show that E{ A2} = v(v + 1) / a2 and consequently that Var{ A} = v / a2 = (1 / v)E{ A}2.

The result derived in Exercise 3.12 has two important implications. The first is a diagnostic tool for the gamma density. That is

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