<p>I think this is a very fundamental confusion.
<span class="math-container">$E[XY]$</span> means that the result of <span class="math-container">$X*Y$</span> should average together to be 0.
Relevant operators are <span class="math-container">$E()$</span>, which is <em>average</em>.</p>
<p>Implications can be very far reaching, but most notably is that (as mentioned above) if
<span class="math-container">$E[XY] \neq E[X]*E[Y]$</span> then <span class="math-container">$X$</span> and <span class="math-container">$Y$</span> 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.</p>

CC BY-SA 4.0
2022-06-16T22:06:00.393Z
2022-06-16T22:06:00.393Z
RegressForward
<p>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.</p>

CC BY-SA 4.0
2022-06-16T15:53:15.600Z
A bit more context would help. Is $E[XY]=0$ an assumption or a result? The same goes for $E[Y]=0$.
Herr K.
CC BY-SA 4.0
2022-06-16T16:37:48.763Z
If $X$ and $Y$ are independent then $E[XY]=E[X]E[Y]$ but not conversely.
Bertrand
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2022-06-16T22:02:35.403Z
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.
tryingtogetsmth
<econometrics><regression>
What does E[XY]=0 mean?
tryingtogetsmth
# What does E[XY]=0 mean?

(Asked by: username_0 on 2022-06-16)

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.

**Tags:** econometrics, regression
> **Comments:**
> **username_1**: A bit more context would help. Is $E[XY]=0$ an assumption or a result? The same goes for $E[Y]=0$.  
> **username_2**: If $X$ and $Y$ are independent then $E[XY]=E[X]E[Y]$ but not conversely.  
> **username_0**: 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.  

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## 1 answers

### Answer by username_3 on 2022-06-16. Score: 2

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.


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