Exercise 8.4.5

$\star$ A probability distribution function $P(x)$ for a random variable $X$ is defined by $P(x) = \Pr\{X \le x\}$. Suppose that we draw a list of $n$ random variables $X_1, X_2, \ldots, X_n$ from a continuous probability distribution function $P$ that is computable in $\O(1)$ time. Give an algorithm that sorts these numbers in linear average-case time.

(UNSOLVED) I don't really understand the math. But the approach is similar to exercise 8.4.4 - we pick a way to partition the buckets so each one is equally likely.