Question 6)

Question 6 Let X1, ..., X: be i.i.d. Exponential (1) random variables. Let Y1, ..., Y be the corresponding order statistics. a) Derive the p.d.f. of Y4. [4] b) Find the joint p.d.f. of S and T, where $ = 4+15 2 2 and T = Y5 - Y4. Remember to describe and sketch the transformed domain. [15]