probability theoryand statistics, two real-valued random variables are said to be uncorrelated if their covarianceis zero.
Uncorrelated random variables have a correlation coefficient of zero, except in the trivial case when both variables have
variancezero (are constants). In this case the correlationis undefined.
In general, uncorrelatedness is not the same as
orthogonality, except in the special case where either "X" or "Y" has an expected value of 0. In this case, the covarianceis the expectation of the product, and "X" and "Y" are uncorrelated if and only ifE("XY) = E("X")E("Y").
If "X" and "Y" are independent, then they are uncorrelated. However, not all uncorrelated variables are independent. For example, if "X" is a continuous random variable uniformly distributed on [−1, 1] and "Y" = "X"2, then "X" and "Y" are uncorrelated even though "X" determines "Y" and a particular value of "Y" can be produced by only one or two values of "X".
Uncorrelatedness is a relation between only two random variables. By contrast, independence can be a relationship between more than two.
Bivariate normal distribution#Correlations_and_independence
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