(i) Given a, b E 2, let T := Va AV, the first visit time to a or b. Assume that a function h : 0 - R satisfies h(a) = 1, h(b) = 0, and h(x) = > Payh(y) for all x * a, b. y Show that (h(XnAT ) )n is a martingale. Provided Pr T 0 for all x * a, b, deduce that h(x) = Px[Va 0 for all x @ A, deduce that g(x) = ExVA