# What does E[XY]=0 mean?

Where X is a regressor and Y is the dependent variable. I know that if E[XY]=E[X]E[Y] then X and Y are independent, hence uncorrelated but I don’t get what E[XY]=0 means.

• A bit more context would help. Is $E[XY]=0$ an assumption or a result? The same goes for $E[Y]=0$. Jun 16 at 15:53
• If $X$ and $Y$ are independent then $E[XY]=E[X]E[Y]$ but not conversely. Jun 16 at 16:37
• Yes sorry, I made a mistake and it’s not E[Y]=0 but, again, E[XY]. Also, exactly, E[XY]=0 is an assumption. Jun 16 at 22:02

I think this is a very fundamental confusion. $$E[XY]$$ means that the result of $$X*Y$$ should average together to be 0. Relevant operators are $$E()$$, which is average.
Implications can be very far reaching, but most notably is that (as mentioned above) if $$E[XY] \neq E[X]*E[Y]$$ then $$X$$ and $$Y$$ are not independent. It is a good mental exercise to attempt to see if you can construct a minimal working example of variables that are independent or dependent.