- Uncorrelated
In

probability theory andstatistics , two real-valuedrandom variable s are said to be**uncorrelated**if theircovariance is zero.Uncorrelated random variables have a correlation coefficient of zero, except in the trivial case when both variables have

variance zero (are constants). In this case thecorrelation is 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, thecovariance is the expectation of the product, and "X" and "Y" are uncorrelatedif and only if E("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.

**ee also***

Correlation

*Covariance

*Bivariate normal distribution#Correlations_and_independence

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