Uncorrelated

In probability theory and statistics, to call two real-valued random variables X and Y uncorrelated means that their covariance is zero.

If X and Y are uncorrelated, their correlation coefficient will also be zero, except in the trivial case when both variables have variance zero (are constants). In this case the correlation is undefined.

In general, uncorrelatedness is not the same as orthogonality, except in the special case where either X or Y has zero expected value. In this case, the covariance is the expectation of the product, and X and Y are uncorrelated if and only if E(XY) = E(X)E(Y'').

If X and Y are independent then they are uncorrelated. It is not true, however, that if they are uncorrelated, then they must be independent. For example, if X is continuous random variable uniformly distributed on [&minus;1, 1] and Y = X2 then they are uncorrelated even though X determines Y, and Y restricts X to at most two values.

Moreover, uncorrelatedness is a relation between only two random variables, whereas independence can be a relationship between more than two.

See also: correlation, covariance

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