$\operatorname{Cov}(\bar X,X_1-X_2)=(\operatorname{Var} X_1-\operatorname{Var} X_2)/n=0$

Let $X_1,X_2,\dots,X_n$ be a random sample from Poisson distribution with parameter $\lambda$. Then covariance between $\bar X$ and $(X_1-X_2)$ is: