Solution
= Solution
The <marginal distributions> have <means> $\mathbb E[X]=p$ and $\mathbb E[Y]=p$. In the joint distribution, $XY$ is nonzero only at $(1,1)$: when $X=1$, the only possible values of $Y$ are $0$ and $1$. Hence
$$
\mathbb E[XY]=pe^{-p},\qquad\boxed{\operatorname{Cov}(X,Y)=pe^{-p}-p^2=p(e^{-p}-p).}
$$
These quantities are finite; for example, $0\leqslant XY\leqslant1$. The <covariance> changes sign when $p=e^{-p}$.