4-20. Verify that the cumulative distribution function given by (4.9):

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

(b) is monotone nondecreasing and continuous in t, with its derivatives existing at every point of continuity of

f, and at each such point dF(t)/dt = f (t)

(c) is continuous from the right

(d) for every pair of real numbers a ≤

b, defines P(a < X ≤

b) =

F

(b) − F(a)

(e) requires limt→−∞ F(t) = 0 and limt→+∞ F(t) = 1