How can I compute the PDF/CDF and expected value of the following function:
$ \frac{\alpha}{r^2} $
where $r$ is generated as follows:
- draw $x$ and $y$ from a uniform distribution in the range $[-r_\max,+r_\max]$.
- if $r_\min \le \sqrt{x^2+y^2} \le r_\max$ then $r=\sqrt{x^2+y^2}$ else repeat step (1)
$r_\min$, $r_\max$, and $\alpha$ are given constants.