10. 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 u, both 0, and the pdf is

a. 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 probability P(a X b).