A family of pdfs that has been used to approximate

Chapter 4, Problem 10

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A family of pdfs that has been used to approximate thedistribution of income, city population size, and size offirms is the Pareto family. The family has two parameters,k and u, both . 0, and the pdf isf(x; k, u) 5 Hk ? ukxk11 x $ u0 x , ua. Sketch the graph of f(x; k, u).b. Verify that the total area under the graph equals 1.c. If the rv X has pdf f(x; k, u), for any fixed b . u,obtain an expression for P(X # b).d. For u , a , b, obtain an expression for the probabilityP(a # X # b).

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