My textbook says:
Let $X$ and $Y$ be two stochastically independent, equally distributed random variables with distribution function F. Define $Z = \max (X, Y)$.
I don't understand what is meant by this. I hope I translated it correctly.
I would conclude that $X=Y$ out of this. And therefore $Z=X=Y$.
How can I interpret $\max(X,Y)$?