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9.3 In the approximation of the random variable $Y$ by $?(X)$, one may use the mean cost $_{?}E{g[Y??(X)]}$, where $g(x)$ is a given function. Show that, if $g(x)$ is an even concave function as below, then the "mean cost" is minimum if $?(X)=E{Y?x}$. You may assume the conditional density of $Y$ given the event ${X=x}$ is symmetric abont its mean, as shown below.