(a) Suppose that is normalized (i.e., Ilw = 1) so that p = min (W) calculates the distance from the hyperplane, defined by B to the, closest in the training data. (Remember, in Lecture note 7, we have the distance for general is Here we assume w = 1 for simplicity.) Argue that (b) Show that ) TW + p, and calculate that BJ jp. (Hint: Use induction.) (c) Show that 119j + II}. (Hint: Use the fact that was misclassified by W which implies yo sign ( (BJ l) T E). Also use the formula that for any a, b = + + 2aTb.) we have lla + bll} (d) Show by induction that + R.2), where R = maxi Ilxi112. (e) Show that (b) and (d) imply t,hat [Hint: Use the Cauchy Schwartz inequality: for any a, b Rd Ila'1211b112.] we have la bl