Question: Let X1, . . ., Xn be a random sample from a Pareto distribution (named after the economist Vilfredo Pareto) with shape parameter a. The

Let X1, . . ., Xn be a random sample from a Pareto (named after the economist Vilfredo Pareto) with shape parameter a. The density function is given by

(The Pareto distribution is a skewed, heavy-tailed distribution. Sometimes it is used to model the distribution of incomes.) Show that the MLE of a is

ra 0 otherwise. In (Xi)

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