Chapter 15.6, Problem 6P

A circular garden bed of radius $1\text{m}$ is to be planted so that $N$ seeds are uniformly distributed over the circular area. Then we can talk about the number $n$ of seeds in some particular area $A$, or we can call $n/N$ the probability for any one particular seed to be in the area $A$.

Find the probability $F(r)$ that a seed (that is, some particular seed) is within $r$ of the center. (Hint: What is $F(1)?$ ) Find $f(r)dr$, the probability for a seed to be between $r$ and $r+dr$ from the center. Find $\bar{r}$ and $\sigma$.