Let X1, ..., Xn be an i.i.d. sample from the Pareto distribution with the density function and cdf f (20) = Oxox -1, x2 20, 0 , F(x) 1 - (xo/2), x 2 20, and 0 , respectively, where To > 0 and 0 > 0. Without assuming that To is given, recall from Tutorial 5 that the mle's of co and A are n To = min { X1, . . ., Xn} and 05 = n respectively. Clog(Xi/To) i=1 It is known that (i) to and es are independent, (ii) to has the Pareto distribution with parameters To and n (Tutorial 2), and (ii) 1/05 has the gamma distribution with parameters "o" = n - 1 and 1 = no.You will use these facts to nd an exact 100(1 (1)296 condence region for $0 and 6. 1. Find P{(:ro/:Eo)\"9 g y} and deduce that the distribution of (1120/1130)m9 does not depend on $0 and :9. What is the distribution of (mo/5150)\"? 2. What is the distribution of mar/9'5? 3. Find a, b, c, and d such that P{c g (so/so)\" g b and c g ate/9'5 g d} = (1 at)? Hint: The answers are not unique. A straightforward approach is to use fact (i) and then place equal probabities in both tails of the distributions you identied in parts 1 and 2. 4. Make use of your answers to part 3 to completely describe an exact 100(1 002% coudence region for :30 and 9