A pdf in the Pareto family is useful for modeling the distribution of wealth in a city, among other things. It has two parameters $\theta$ and $k$, which are positive constants. The pdf is below:
$f(x; k, \theta) = \begin{cases} \frac{k\theta^k}{x^{k+1}} & , x \ge \theta \\ 0 & , x < \theta \end{cases}$
(a) Verify that the above $f$ is a legitimate pdf.
(b) Find $P(X \le b)$, where $b > 0$ is some constant.
