Chapter 15.6, Problem 8P

Given that a particle is inside a sphere of radius 1, and that it has equal probabilities of being found in any two volume elements of the same size, find the cumulative distribution function $F(r)$ for the spherical coordinate r, and from it find the density function $f(r).$ Hint: $F(r)$ is the probability that the particle is inside a sphere of radius r. Find $\bar{r}$ and $\sigma$.