Two independent random variables, $X$ and $Y$, are uniformly distributed on the unit interval (-1,1).
- Determine the density for $U=min(X,Y)$ and for $W=max(X,Y)$
- Find the expectation for each variable $(U $ and $ W)$
- Find variance of each variable ($X,U,$ and $W)$
- Find the variance of $(U + W)$
I know that $U$ and $W$ are dependent on each other. I want to understand how to get the first question since if I understand that, I should be able to get the second one. I also think I will understand how to get variance of $U$ and $W$ but not for $X$. Thanks for whomever helps.