The famous formula for PDF for the distance $r$ between two points that are part of the (homogenous) spatial PPP with density $\lambda$ is
$$f(r) = 2\pi\lambda re^{-\pi\lambda r^2}$$
I need to find the Area for the given system, which then, of course, depends on the random variable $r^2$. How can I find the PDF for the $r^2$?
$$f_A = r^2$$
Note that $0<r\leq200$ and $r$ has a unit in meteres
$$P(R \le r)= \int_{-\infty}^r f_R(t)\, dt$$
let $y> 0$, $$P(R^2 \le y)=P(R \le \sqrt{y})= \int_{-\infty}^{\sqrt{y}} f_R(t)\, dt$$
$$f_{R^2}(y)=\frac{d}{dy}\int_{-\infty}^{\sqrt{y}}f_R(t)\, dt = f_R(\sqrt{y}) \frac{d}{dy}\sqrt{y}=\frac{f_R(\sqrt{y})}{2\sqrt{y}}$$