3. In class we found the optimal linear predictor of Y based on X = x. The criterion for optimality was minimum mean squared error. In this problem, we will find the best predictor, allowing for non- linear predictors as well. Toward this end, let Y = g(X) be the best predictor (where g may now be non-linear). Notice that the goal is to minimize E (Y - 9(X)) ?] = [(y - 9(z) Prix(y | z) PX(I). (5.2) I.y Argue that each term of the sum above can be minimized independently, and that the minimum is given by the conditional expectation