4-19. Verify that the cumulative distribution function given by (4.3):

(a) has values restricted to [0, 1]

(b) is monotone nondecreasing

(c) is continuous from the right

(d) defines P(Xs < X ≤ Xt) = F(Xt) − F(Xs)

(e) requires at points of discontinuity X = Xi, i = 1, 2, . . . , that F(Xi+0)−

F(Xi − 0) = F(Xi) − F(Xi − 0) = f (Xi)

(f) requires limXi→−∞ F(Xi) = 0 and limXi→+∞ F(Xi) = 1