2. Let X1, ..., Xn be a random sample from U(0,8 + 1) distribution, where - < 0<. Let U = min{X1, ..., Xn} and V = max{X1, ... , X,}. (a) Prove that T = (UV) is a sufficient statistic (for 8). (b) Derive the joint distribution of U and V. (Use Theorem 5.4.6 in Casella-Berger; also look at Example 5.4.7.) (c) Let R=V-U. Derive the joint pdf of U and R, using transformation of variables approach (a) Find the (marginal) distribution of R. (e) Derive the conditional distribution of R given U.