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 theta, both > 0, and the pdf is as follows. f(x; k, theta) = k · thetak xk + 1 x ≥ theta 0 x < theta Verify that the total area under the graph equals 1. [infinity] k · thetak xk + 1 dx theta = [infinity] theta = 0 − thetak = (c) If the rv X has pdf f(x; k, theta), for any fixed b > theta, obtain an expression for P(X ≤ b). (d) For theta < a < b, obtain an expression for the probability P(a ≤ X ≤ b).