what happens when I have the following MGF with the $N$ and $M$ independent: $$ E(e^{-\rho R N M}),\mbox{ with }N \sim \mbox{Poisson} (\lambda), M \sim \mbox{Exponential} \left(1/t,1/t^2\right).$$
A tip I got was to use the tower property of expectations to condition on e.g. $M$ and to search for the MGF for compound Poisson, however I have to admit it only further confused me. Grateful for any help solving that MGF.