We have $n$ independent variables, $X_1, X_2, \ldots , X_n$ uniformly distributed over the interval $(0,1)$. We then define two new variables, $M = \min(X_1, X_2, \ldots , X_n)$ and $N = \max(X_1, X_2, \ldots , X_n)$.
I want to find the joint distribution of a pair $(M,N)$. I also want to find the CDF for $M$ and the CDF for $N$. What I'm confused about is how these even have distributions. Isn't there one unique value for M and one unique value for $N$?