Let the independent r.v.'s X1,. .., Xn be distributed as U(0, 1), and let 1 j n. Use the relevant results in Example 3, and Exercise 1.6(i) in order to derive:
i) The conditional p.d.f. of Yj, given Y1;
ii) The conditional p.d.f. of Yj, given Yn;
iii) The conditional p.d.f. of Yn, given Y1; and the conditional p.d.f. of Y1, given Yn.