Rather than attempt to derive a general expression for the distribution of $X + Y$ in the discrete case, we shall consider some examples. (Ross, A First Course in Probability, Section 6.3.4)
The examples in the book are sum of two
- Binomial random variables : itself a Binomial
- Poisson random variables: itself a Poisson.
Is there anywhere else I should look for further details on the topic? Or is the general formula too difficult/not important?