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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 ...
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.