A family of pdfs that has been used to approximate the distribution of income, city population size,

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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 , and the pdf is

a. Sketch the graph of .

b. Verify that the total area under the graph equals 1.

c. If the rv X has pdf , for any fixed , obtain an expression for .

d. For , obtain an expression for the probability P(a # X # b).

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