Let $X$, $Y$ be independent random variables with the common pdf \begin{eqnarray*} f(u) &=& \left\{\begin{array}{ll} u\over2 & \mbox{for } 0 < u < 2\\ 0 &\mbox{elsewhere} \end{array}\right.\\ \end{eqnarray*} Set up an explicit double integral for $P(X Y > 1)$
Let $Z$ be the maximum of $X,Y$ (That is, $Z = X$ if $X \geqslant Y$, and $Z= Y$ if $Y > X$). Find $P(Z\leqslant 1)$
Find the pdf $g(z)$ of $Z$, being sure to define $g(z)$ for all numbers $z$.
This is a problem on a practice exam I'm studying, but I really have no idea how to approach the problem.