In the statistics lecture that I'm attending, the professor once used the following: $X, Y$ random variables and i.i.d., then $$\mathbb{E}(XY) = \mathbb{E}(X)\mathbb{E}(Y)$$ I was trying to see an argument why this should be the case, but I could not find one. Why exactly am I allowed to do this?
Thanks for every answer!