6.18 Show that the statistics X(1) and [Xi − X(1)] of Problem 6.17

(c) are independently distributed as E

(a, b/n) and bGamma(n − 2, 1) respectively.

[Hint: If a = 0 and b = 1, the variables Yi = (n − i + 1)[X(i) − X(i−1)], i = 2,...,n, are iid as E(0, 1).]