I have an idea of how to do this but I'm not sure if this is the right direction.
A stick of length $1$ is broken into $2$ pieces at a random point. Find the correlation coefficient and the covarience of the pieces.
I let $X$ be the length of the first piece and $Y$ be the length of the second piece, and I have come to conclusion that $P(X=x)=1-y$ and $P(Y=y)=1-x$ but for some reason it doesn't seem right to me. I know I need to find $E(XY)$, $E(X)$, and $E(Y)$ for the covarience but I'm just feeling skeptical about $P(X=x)=1-y$ and $P(Y=y)=1-x$. Did I do this right?