Solve the following:

(a) Let X be a random variable with charactheristic function p. Suppose that P(X E hZ) = 1, with some h > 0. Show that h . TT / h P ( X = a) = e-itx 'p(t) dt for a E hZ. 2TT J -T/ h (b) Suppose now that P(Y E b + hZ) = 1 with be [0, h). Using part (a), show that the previous formula holds for Y with a E b + hZ