Let $X_{1},X_{2},...,X_{n}$, for $n=2,3,...,$ be independent and identically distributed random variables with common distribution function. $F_{X}$ . Find a formula for the joint distribution $F_{Y,Z}$ for
$Y=\max\{X_{1}, X_{2},...,X_{n}\} \quad \text{and} \quad Z=\min\{X_{1},X_{2},...,X_{n}\}$
in terms of $F_{X}$.