2.17 By making the transformation UnFX(X(1)), Vn[1FX(X(n))] in (2.6.8) with r1, sn, for any continuous FX, show

2.17 By making the transformation U¼nFX(X(1)), V¼n[1FX(X(n))] in

(2.6.8) with r¼1, s¼n, for any continuous FX, show that U and V are independent random variables in the limiting case as n ! 1, so that the two extreme values of a random sample are asymptotically independent.