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3. [2pts] Benefit of Averaging. Consider m predictors h1, ..., hm, each of which accepts an input r and produces an output y, i.e., y = h,(x). Consider the squared error loss function L(y, t) = (y - t)2. Show that the loss of the average estimator m h(x) = 1 E hi(I) , m i=1 is smaller than the average loss of the estimators. That is, for any x and t, we have m L(h(I), t) L(hi(x), t). m i=1 Hint: Use the fact that for any discrete random variable D with finitely many states, we have E[D'] - E[D]2 = Var[D] 2 0. (0.1)