(h) For any pair of finite variance random variables (X, Y), the conditional expectation E[Y|X] is a function of X that is known to satisfy the following property: for all functions E[(Y - E[YIXI)$(X )] = 0. Using this definition, prove that the mean squared error E[(Y -6(X))"] of estimating Y from X is minimized by choosing o(X) = E[Y |X]. Le., the conditional expectation minimizes the mean squared error of estimation. Hint: Think about how we proved the orthogonality principle without necessarily trying to formally define a subspace