I didn't know why I compute $E(XY)$ wrongly. $$X=(1, 2, 0.5, -1),\qquad Y=(-2, 1, -0.5, 2).$$
$$E(XY) = \frac{-2 + 2 -0.25 -2}{4} = -0.5625\text{ (incorrect)}$$
because $\operatorname{Cov}(X,Y)=-0.8542$, $E(X)=0.625$, $E(Y)=0.125$ so $E(XY)$ should be $-0.1042$.
$X=1$ and $Y=-2$ gives $XY=-2$
$X=1$ and $Y=1$ gives $XY=1$
Repeat this for every pair $(X,Y)$ to find all outcomes. Average them over the total number to find $E(XY)$.
I think there's a way to compute it without calculating all the pairs, but this calculation is how $E(XY)$ is defined.
For the calculation, I would use $Cor(XY)+E(X)E(Y)=E(XY)$.