A family of pdf’s that has been used to approximate the

Chapter 5, Problem 10E

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A family of pdf’s that has been used to approximate the distribution of income, city population size, and size of firms is the Pareto family. The family has two parameters, ?k ?and , both >0, and the pdf is a.? ?Sketch the graph of f ? ? ? ?k?, ?). b.? ?Verify that the total area under the graph equals 1. c.? ?If the rv ?X ?has pdf? f ?(?x?; ?k?, ?), for any fixed b > ? obtain an expression forP(X?b). d.? ?For ?P(?a ??? ?? ?b? .

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