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In
probability theory and
statistics, to call two real-valued
random variables ''X'' and ''Y'' '''uncorrelated''' means that their
correlation is zero, or, equivalently, their
covariance is zero.
If ''X'' and ''Y'' are
independent then they are uncorrelated. It is not true, however, that if they are uncorrelated, they must be independent. For example, if ''X'' is
uniformly distributed on [-1,1] and ''Y''=''X''
2 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
