# Expectation value and variance of the sum of random variables with conditions

Let $$X_1,X_2,\dots,X_n$$ be independent and identically distributed Poisson random variables and define the partial sums $$S_n=\sum\limits_{i=1}^n X_i$$.

I would like to calculate the expectation value $$\mathbb{E}(S_n)$$ and variance $$\text{Var}(S_n)$$.