Question: A random sample X1, ..., X, is drawn from a Pareto distribution with PDF f(x | 0, 0) = I(x > a), for parameters #

A random sample X1, ..., X, is drawn from a Pareto distribution with PDF f(x | 0, 0) = I(x > a), for parameters # > 0 and known a > 0. (a) Show that V(0, X) = 20_:, log(X,/a) is a pivot quantity with a x, distribution and find the correct value for the degrees of freedom v. (b) Using (a), find a 100(1 - a)% confidence interval for 0. (c) Invert your confidence interval to create a size-o test for the hypotheses Ho : 0 = 1 vs H1 : 0 # 1

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