$E(XY)=E(X)E(Y)\neq 0$ implies independance I have a little question.
I know that $E(XY)=E(X)E(Y)$ does not imply independence. There are a lot of examples with $E(XY)=E(X)E(Y)=0$.
But if $E(XY)=E(X)E(Y)\neq 0$, is it implying that $X$ and $Y$ are independent ? If not, have you an example where $X$ and $Y$ are dependent ?
Thanks a lot !

Since $E(XY)-E(X)E(Y)$ doesn't change if you add a constant to one or both of $X,\,Y$, any dependent $X,\,Y$ with $E(XY)=E(X)E(Y)=0$ can be shifted (thereby preserving their dependence) to give $E(XY)=E(X)E(Y)\ne0$.
