Question: By Jensensinequality, convexfunctionssatisfy E[g(Y )] g[E(Y )]. Usethistoprovethat for concavefunctions, E[g(Y )] g[E(Y )]. Applytheappropriatecasesto log(Y ) and 1~Y for a positively-valuedrandomvariable Y

By Jensen’sinequality, convexfunctionssatisfy E[g(Y )] ≥ g[E(Y )]. Usethistoprovethat for concavefunctions, E[g(Y )] ≤ g[E(Y )]. Applytheappropriatecasesto log(Y ) and 1~Y for a positively-valuedrandomvariable Y .

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