Say we have two random variables $X,Y$ (that is all we know) and a new random variable $Z = \max(X,Y)$
Those random variables have distribution functions $F^X$, $F^Y$ and $F^Z$.
The question where I'm stuck is:
Write $P(X \leq x)$, $P(Y \leq y ) $ and $F^Z$ down in dependance of $F^X$ and $F^Y$.
Any tips for this problem are appreciated. Full answers discouraged.