Let $X$ and $Y$ be independet Poisson random variables with parameters $\lambda$ and $\mu$.
I have to calculate $E((X+Y)^2)$ .
What I did: $E[(X+Y)^2]=E[X^2]+E[Y^2]+2EXEY$
I know that $2EXEY=2\lambda\mu$, but I don't know how to calculate the squared expected values.
Thanks in advance!