A family of pdfs that has been used to approximate the
Chapter 4, Problem 4.18(choose chapter or problem)
A family of pdfs 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 f(x; k, ) k x k 1 k x 0 x a. Sketch the graph of f(x; 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 for P(X b). d. For a b, obtain an expression for the probability P(a X b). 4
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