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Let X1, . . . ,Xn be an i.i.d. sample from the Pareto distribution with the density function f(:t:) : Exam6'1, m 2 3:0, Where

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Let X1, . . . ,Xn be an i.i.d. sample from the Pareto distribution with the density function f(:t:) : Exam6'1, m 2 3:0, Where 330 > 0 and 6 > 0. Assume that :30 is given. Let Y7; = log(X,-/a:0), i = 1, . . . ,n. 1. Find 93, the method of moments estimate of 6 based on Y1, . . . , Y\". 2. Find the distribution of i7. 3. Find the mean and variance of 93

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