----------

This question doesn't seem as straightforward as it sounds. For example, I have tried using the convolution formulas here, but can't seem to find a closed form expression for the integral. I have also tried multiplying the moment generating functions (mgfs) of [math]X[/math] and [math]Y[/math], but it does not seem to match up to any known mgfs.

Does anyone have any ideas on how to find the distribution for [math]Z[/math]?