A family of pdf’s that has been used to approximate the distribution of income, city pop...

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 (x; k, θ).

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

c. If the rv X has pdf f (x; k, θ), for any fixed b > θ obtain an expression forP(X≤b).

d. For θP(a ≤ X ≤ b).