$X\sim\operatorname{Pois}(2)$ and $Y\sim\operatorname{Pois}(5)$ are independent. How to obtain the mean and variance of $X-Y$?

Question

If both random variables X and Y are Poisson then their mean is equal to their variance respectively. I thought of subtracting both means but I realise, how was I going to get the variance. Poisson distribution=(μ^x.e^-μ)÷(x!). Where μ= mean, X can assume any number.

Answer 1

Because $X,Y$ are Poisson,

$$E(X)=Var(X)=2\\ E(Y)=Var(Y)=5$$

Thus

$$E(X-Y)=2-5=-3\\ Var(X-Y)=2+5=7$$