Finding CDF from PDF I need to find the CDF from a given PDF.
The PDF is given by
$f_R(r)=2\lambda\pi r\exp(-\lambda\pi r^2)$.
What is its corresponding CDF $F_Y(y)$?

$$
f_R(r)=2\lambda\pi r\exp(-\lambda\pi r^2)
$$
This function is non-negative only if $r\ge0$.  We have
$$
\int_0^\infty \exp(-\lambda\pi r^2) (2\lambda\pi r \,dr) = \int_0^\infty \exp(-u) \, du = 1,
$$
so the support must be all of $[0,\infty)$.  The c.d.f. is
$$
F_R(r) = \Pr(R\le r) = \int_0^r \exp(-\lambda\pi s^2) (2\lambda\pi s \,ds) = \int_0^{\lambda\pi r^2} e^{-u} \, du = 1 - e^{\lambda\pi r^2} \text{ for } r \ge 0.
$$
