Question: 2.49. (Sec. 2.5) Show that for any function h(X(2) and any joint distribution of Xi and Xl2l for which the relevant expectations exist, J'[Xi -

2.49. (Sec. 2.5) Show that for any function h(X(2») and any joint distribution of Xi and Xl2l for which the relevant expectations exist, J'[Xi - h(X{2))f = J'[Xi -

g(X(2»)]2 + J'[g(X(2») - h(X(2»)]2, where g(X(2») = J'Xj IX(2) is the conditional expectation of Xi given X(2) = x(2). Hence g(X(2») minimizes the mean squared error of prediction. [Hint: Use Problem 2.48.]

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