7.37. (Sec. 7.5) Show that if X~-I and X~-z are independently distributed, then x~· I X~ z is distrihuted ~s (:d'l ,l" /4. [Hint: In the joint density of x = X~-I and y = x.~ _ z substitute z = 2/;;, x = x, and CXPI ess the marginal density of z as z'\" .1h(Z)' where h(z) is an integral with respect to x. Find h'(z), and solve the difflon:ntial L'quation. Sec Srivastava and Khatri (J 979), Chapter 3.]