In probability theory class I was asked the following question:
Let X,Y be two random variables (could be discrete or continuous) such that they are mean independent, that is for all $ y \in \mathbb{R} $ we have the equality: $ E[X|Y=y] = E[X] $ and we are asked to prove or give a counterexample that X and Y are independent random variables.
I figured since I tried to prove it but could not succeed so I am inclined to think that it is false but I cannot find a counterexample. Could someone then please provide an example of random variables that are dependent but mean independent? Thank you all.