Suppose that X1, . . . , Xm form a random sample of m observations from a continuous distribution for which the p.d.f. f (x) is unknown, and that Y1, . . . , Yn form an independent random sample of n observations from another continuous distribution for which the p.d.f. g(x) is also unknown. Suppose also that f (x) = g(x − θ) for −∞ < x <∞, where the value of the parameter θ is unknown (−∞ < θ < ∞). Let F−1 be the quantile function of the Xi ’s, and let G−1 be the quantile function of the Yj ’s. Show that F−1(p) = θ + G−1(p) for all 0 < p < 1.