1. If $X$ and $Y$ follow Poisson distributions and are independent then $X+Y$ also follows a Poisson distribution.

In particular, if $X\textasciitilde{}Po( \lambda )$ and $Y\textasciitilde{}Po( \mu )$ are two independent distributions, then $X+Y\textasciitilde{}Po( \lambda + \mu )$.

The random variables, $R\textasciitilde{}Po(2),S\textasciitilde{}Po(3)andT\textasciitilde{}Po(4)$ are independent.

Write down the distribution of:

(i) $R+S$

(ii) $S+T$