I'm confused on what the $\min$ means. For example if I need to find the distribution function of $\min(X,Y)$ what am I looking for exactly? Am I looking for the distribution of the minimum value of either $X$ or $Y$. As an example lets just say that $X$ can have the values $\{1,2,3,5,8,13\}$ and $Y$ can have the values $\{3,4,6,7,8,12,24\}$. If were finding the $\min(X,Y)$, how do I do that? I think this is a legitimate example, if not you can fill in the blanks or use whatever you need to. I just dont understand when I see a problem ask for the distribution of $\min(X,Y)$.
I'm aware that theres also $\max(X,Y)$ as well but I'm just choosing $\min$ for the sake of this post. I'm assuming the same procedure goes for $\max$ as $\min$.