I wonder how to solve this question

Let X1, . . . , X" be a random sample from a population with pdf 6'9\"\"), :1: 2 0, f(w|9) = { 0, 3(9, where 0 > 0. Find the shortest 1 a condence interval for 0 of the form [X (1) + a,X(1) + b], where X\") = min{X1, . . . ,Xn} and a g b are real numbers