Mean dependence
In probability theory, a random variable Y {\displaystyle Y} is said to be mean independent of random variable X {\displaystyle X} if and only if its conditional mean E ( Y ∣ X = x ) {\displaystyle E(Y\mid X=x)} equals its (unconditional) mean E ( Y ) {\displaystyle E(Y)} for all x {\displaystyle x} such that the probability density/mass of X {\displaystyle X} at x {\displaystyle x} , f X ( x ) {\displaystyle f_{X}(x)} , is not zero. Otherwise, Y {\displaystyle Y} is said to be mean dependent on X {\displaystyle X} .