Refer to the pdfs given in Exercise 6.9. For each, let X(1) < . . . < Xn-1) be the ordered sample, and define Yi = X(n) - X(i), i = 1,..., n - 1.
a. For each of the pdfs in Exercise 6.9, verify that the set (Y1,..., Yn-1) is ancillary for θ. Try to prove a general theorem, like Example 6.2.18, that handles all these families at once.
b. In each case determine whether the set (Y1,..., Yn-1) is independent of the minimal sufficient statistic.