Again suppose that independent observations z1, 72, from the Pareto distribution with pdf ,In are available S(z\3) = on r > 1, with 3>0. You showed in Question 2 that e(3) = n log 3 – (3 + 1) log a....

Extracted text: Again suppose that independent observations z1, 72, from the Pareto distribution with pdf ,In are available S(z\3) = on r > 1, with 3>0. You showed in Question 2 that e(3) = n log 3 – (3 + 1) log a. and that the MLE of ß is E, log X; (a) For this Pareto distribution, it is known that E() - and V(log X) Using these results, show that is a consistent estimator of . Explain your reasoning. (b) Using the logged version of the Fisher-Neyman Factorisation Theorem, show that C log X, is a sufficient statistic for 3. (c) Is ! a sufficiet statistic for 8? Justify your answer.