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Prove the following analogs to Stein's Lemma, assuming appropriate conditions on the function

`g`

. (a) If

`x∼\gamma (\alpha ,\beta )`

, then

`E(g(x)(x-\alpha \beta ))=\beta E(xg^(')(x)).`

(b) If

`x∼\beta (\alpha ,\beta )`

, then

`E[g(x)(\beta -(\alpha -1)((1-x))/(x))]=E((1-x)g^(')(x))`