Thanks so much @chiro and @bpet. I'm still a bit loss. So you're recommendation is to start with one arbitrary characteristic function that is hopefully decomposable and see if I can craft another one?
Thanks again.
I am wondering if I can find a decomposition of Y that is absolutely continuous nto two i.i.d. random variables X' and X'' such that Y=X'-X'', where X' is also Lebesgue measure with an almost everywhere positive density w.r.t to the Lebesge mesure.
My main intent is to come up with two i.i.d...