Let $X= \min( U, V)$ and $Y= \max(U, V)$ for independent uniform $(0,1)$ variables $U$ and $V$. Find the distribution of $Y-X$.
I'm studying for Exam P with Pitman's text Probability. This is from 5.2.13.
I know the answer is $2(1-x)$ but I'm not sure how to start. I'm looking for a simple approach as I already found a complicated explanation to this problem.
I guess I'm going to have to settle with viewing it as points in a plane. I thought it was simpler than this. Thanks again.