I'm trying to workout a multivariate transformation of multiple random variables on Maple 17. I know how to work out for a single variable but couldn't get it to work for two variables. I'm trying to workout the following question.
$f(x,y) := \left\{ \begin{array}{ll} 12xy(1-y) & 0< x< 1,0< y< 1 \\ 0 & elsewhere \\ \end{array} \right. \ $
Where the joint transformation of $(X,Y)$ is $Z=XY^2$ and $W=Y$