Suppose that you have two random variables $X$ and $Y$, of unknown distribution and that are not independent but uncorrelated. Both $X$ and $Y$ have zero expectation.

I am looking for upper bounds or statements about $$ \mathbb{E}[X\,|\,X+Y=z]. $$

The case for Gaussianity is addressed here.


  • 2
    $\begingroup$ if $f$ is the joint pdf of $X$ and $Y$ (the two being not independent) $$\mathbb{E}(X | X+Y=z) = \frac{1}{\int_{-\infty}^\infty f(x,z-x) dx} \int_{-\infty}^\infty x f(x,z-x) dx$$ $\endgroup$ – reuns Jan 4 '16 at 9:31

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.