I am having difficulty resolving the two exercises below

1)Consider the function
[IMG][/IMG]
Find the E(X).
I now is a Poisson(y), but i don't know how to find this expectation

2)Consider an experiment with three possible outcomes that occur with a probability p1, p2, p3 respectively. Suppose that take place independent repetitions of the experiments and Xi is the number of times that the outcome i occurred.
i) Find the density of X1 + X2
ii) Find P (y = X2 / X1 + X2 = z) y, .... z.

I know it is a multinomial, but do not know how to find the density, to be honest I'm struggling to find exercises that require density function.