Let X, , X 2 , • • • , x., be a random sample of size n = S from the normal distribution N(O, 9).
(a) Argue that the ratio R = (X + Xi)/(Xi + · ··+ ..¥;) and its denomi nator (Xi + ··· + ..¥;) are independent.
(b) Does SR/ 2 have an £-distribution with 2 and S degrees of freedom? Explain your answer.
(c) Compute E(R) using Exercise 7.60.