$f(x,y) = {2\over 5}(2x+3y) \quad for\quad 0
and we want to know the distribution of $2X+3Y$
I did it in a very lousy way which is let $ U=2X+3Y ,\; V=X$
Then have $\;f_{U,V}(u,v)$ and then integer by V to get $\;f_U(u)$
So I tried $f_{U,V}(u,v) = f_{X,Y}(v,{u-2v\over 3})*{2\over5}={2u\over 15}$
$\int_0^\infty{2u\over 15}dv=$ then I think i might be wrong here....