Question: Let X and Y be random variables with finite means. (a) Show that where g(x) ranges over all functions. (E(Y|X) is sometimes called the regression

Let X and Y be random variables with finite means.
(a) Show that

where g(x) ranges over all functions. (E(Y|X) is sometimes called the regression of Y on X, the "best" predictor of Y conditional on X.)
(b) Show that equation (2.2.4) can be derived as a special case of part (a).

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