Let F be a continuous strictly increasing c.d.f. with p.d.f. f . Let V have the uniform distribution on the interval [a, b] with 0 ≤ a < b ≤ 1. Prove that the p.d.f. of X = F−1(V) is f (x)/(b − a) for F−1(a) ≤ x ≤ F−1(b). (If a = 0, let F−1(a) = −∞. If b = 1, let F−1(b) = ∞.)