9. Consider n tosses with a biased die, for which the probabilities of 1, . . . , 6 points are given by 1 1 - 8 12 2 2 -8 12 3 3 - 8 12 4 1 + 8 12 5 2+8 12 6 3+8 12 and let X; be the number of tosses showing i points. (i) Show that the triple ZI = XI + Xs, Z2 = X2 + X4 , Z3 = X3 + X6 is a maximal ancillary; determine its distribution and the distribution of XI"'" X6 given ZI = ZI' Z2 = Z2 ' Z3 = Z3 ' (ii) Exhibit five other maximal ancillaries. [Basu (1964).)