Solution
= Solution
A spherical shell contributes a factor $4\pi r^2$ to the number of stars. Since $\int_0^\infty r^2e^{-r/r_0}dr=2r_0^3$, the normalized distance density is
$$
p(r_s)=\frac{r_s^2}{2r_0^3}e^{-r_s/r_0},
\qquad r_s>0.
$$
Thus $C=(2r_0^3)^{-1}$, $\alpha=2$, and $\beta=1$. This is a <gamma distribution> with shape three and scale $r_0$.