# What's an example where the expectation of product is zero but not conditional mean?

I am studying linear regressions. In this business, sometimes we can prove the results we want with the assumption that the error term $$U$$ is such that $$E(XU) = 0$$. But for lots of other results, in special the ones that require a causal interpretation, we need to assume $$E(U|X) = 0$$.

I understand how the latter implies the former. But I am struggling with an example where the first is verified while the second is not. Can anyone provide some intuition/counter-example? Thanks a lot in advance!

Consider $$X$$ uniform in $$[-1,1]$$ and $$U = |X|$$. Would you allow that as a counter-example, even though very artificial?