Please answer both parts of question with detailed proofs.

(10 points) Consider the following general model for the training data (thi), '5 = 1, . . . ,n in a learning problem: 1'? = Has) + fr, 2 where f is the true mean response function; and the random errors a; have mean zero, variance 0 , and are mutually independent. We discussed this model in the class. Let f be the estimator of f obtained from the training data. Further, let ($0,113) be a test observation. In other words, so is a future value of :1: at which we want to predict Y and Ya is the corresponding true value of Y. The test observation follows the same model as the training data, i.e., H} = f(1'0) + 60' \\fhereAEo has the same distribution as the 61' for the training data but so is independent of the 61;. Let Y0 = f (3:0) be the predicted value of YE). (a) Show that MSE{f(ttn)} = (Between)? +var{f(to)}- (b) Show that Elf/0 m2 = (Between)? + vat{fee} + az