I'm working on some statistics project and am not getting further because of some stupid prediction that doesn't want to be 0. That's why I was wondering if maybe the following holds: Suppose we have a random variable X and an unknown constant m. Is then $$E\left(X|X+m\right)=E(X)?$$ That would help a lot. I thought it might hold because m is unknown and thus knowing X+m doesn't say anything about X, so one could consider X and X+m as being independent?
Thanks a lot!