Question: 6. A random sample X1 , . . . , Xn is drawn from a Pareto distribution with PDF f(x|,)= x 1I(x>), (a) Derive the

6. A random sample X1 , . . . , Xn is drawn from a Pareto distribution with PDF f(x|,)= x 1I(x>),

(a) Derive the LRT and show that the rejection region has the form R = {T < c1 or T > c2} where the test statistic is T = Pni=1 log(Xi/) = Pni=1 log(Xi). (b) Show that under H0, the distribution of 2T follows

a 2 and find the degrees of freedom . How can you use this to find the values of c1 and c2?

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