I have a joint distribution function
f(x,y)=12xy(1-y), 0<x<1, 0<y<1
and need to determine the distribution of Z=X+2Y.
I know that I can do this by finding F(Z) over different regions (i.e. 0<z<1, 1<z<2, 2<z<3) and then differentiating for f(z), but am having some trouble figuring out what my different regions of integration should be. Any help would be greatly appreciated.