9. (a) Let X be an exponential random variable. Show that P(X > s+t|X > s) =P(X > t) for all s, t > 0. (b) Let X be a random variable having support [0, co) and a cdf F differentiable on (0, co). Suppose that X satisfies P(X > s+t|X > s) = P(X > t) for all s, t > 0. Show that & In { 1 -F(x) } is a constant for x > 0. Hence show that X is an exponential random variable