Let X1, ..., Xn be an i.i.d. sample from the Pareto distribution with the density function and cdf Oxox-0-1 f(2) = 1 - (xox), x2 x0, Lo, and F(x) 0 , x 0 and 0 > 0. Without assuming that To is given, recall from Tutorial 5 that the mle's of co and 0 are n To = min {X1, . .., Xn} and 05 = - n respectively. log (Xi/Xo) i=1 It is known that (i) To and 05 are independent, (ii) zo has the Pareto distribution with parameters co and no (Tutorial 2), and (iii) 1/05 has the gamma distribution with parameters "a" = n - 1 and 1 = no.You will use these facts to nd an exact 100(1 a)2% condence region for 330 and 9. 1. Find P{($0/:E0)\"9 S y} and deduce that the distribution of (:130 /:1":0)\"6 does not depend on 230 and 6. What is the distribution of (mo/i0)\"9? 2. What is the distribution of 2719/ 95? 3. Find a, b, c, and d such that P{a S (mo/5:0)\" S b and c S 2110/95 S d} = (1 002. Hint: The answers are not unique. A straightforward approach is to use fact (i) and then place equal probabilities 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 a)2% condence region for $0 and 9