7. Suppose T has a discrete distribution, with p.m.f. f(w;) = P[T = wj] = pj j = 1, 2,..., where 0w1 < W2 < are known. Then the hazard function can be defined as hj = P(T = w;|T w;) for j = 1, 2,... Using this notation, show that the p.m.f. and survivor function for T can be expressed as f(t) = h; (1-h) for t = wj 1=1 0 Wj otherwise and S(t) = j s.t. wjt