In probability theory, a random variable
is said to be mean independent of random variable
if and only if its conditional mean
equals its (unconditional) mean
Stochastic independence implies mean independence, but the converse is not true.
;[1][2] moreover, mean independence implies uncorrelatedness while the converse is not true.
Unlike stochastic independence and uncorrelatedness, mean independence is not symmetric: it is possible for
The concept of mean independence is often used in econometrics[citation needed] to have a middle ground between the strong assumption of independent random variables (
) and the weak assumption of uncorrelated random variables
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