Question: This is a continuation of Tutorials 2 and G. Let Xi, ..., X. be an i.l.d. sample from the Pareto distribution with the density function

This is a continuation of Tutorials 2 and G. Let Xi,

This is a continuation of Tutorials 2 and G. Let Xi, ..., X. be an i.l.d. sample from the Pareto distribution with the density function and cdf and F() = respectively, where , 5 0 and # 3 0. Without meraming that r, is given, recall from Tutorial & that the male's of 2, and 4 are To = min{X]..a, Kn) and i = n. respectively. It is known that (i) Fo and 4 are independent, (ii) To has the Fareto distribution with parameters ag and of (Tutorial 2), and (1) 1/4's has the gamma distribution with parameters "a" - n - 1 and ) - ne. "Upload to LumiNUS > Film > Amoments '> Upload - AL You will use these facts to find an exact 100[1 - a] % confidence region for so and &. 1. Find P{(m/i)"Su) and deduce that the distribution of (re/Fo]" does not depend on as and 9. What is the distribution of (10/Po)? 2. What is the distribution of 2ne/67 3. Find a, b, c, and d such that Plas (n/i)"

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