Let F(x) be the cdf of the continuous-type random variable X, and assume that F(x) = 0 for x ≤ 0 and 0 < F(x) < 1 for 0 < x. Prove that if P(X > x + y | X > x) = P(X > y), then F(x) = 1 - e⁻⋋ˣ, 0 < x.
Hint: Show that g(x) = 1 - F(x) satisfies the functional equation g(x + y) = g(x)g(y), which implies that g(x) = aᶜˣ