Question: Let X 1,. . . ,Xn he an i.i.d. sample from the Pareto distribution with the densitj,r function f{.r] = Hiram'94, :r 13 In, where

Let X 1,. . . ,Xn he an i.i.d. sample from the Pareto distribution with the densitj,r function f{.r] = Hiram'94, :r 13 In, where In :a U and H :3 0. Assume that In is given. Let Y : log(Xif:r:), i = 1,. . . , a. 1. Find $3, the method of moments estimate of I? based on Y1, . . . , Y\". 2. Find the distribution of 1\". 3. Find the mean and variance of F3. You may assume that n E 3 and use the following facts: {a} 1"[o:+ 1} 2 came} for o: I} 0. {b} If U follows a gamma. distribution, then EH5\") = not + TNFK'HHH for r I} o

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4. Similarity (representativeness).

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