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The correlation between two random variables $X$ and $Y$ is a measure of the degree of linear association between them. The correlation is defined as

$$ {\rm cor}(X,Y) = \frac{ {\rm cov}(X,Y) }{ \sqrt{ {\rm var}(X) {\rm var}(Y) } },$$

where ${\rm cov}(X,Y)$ denotes the covariance between $X$ and $Y$.

The correlation coefficient is bounded between $-1$ (perfect negative linear relationship) and $1$ (perfect positive linear relationship). If $X$ and $Y$ are independent, we have ${\rm cor}(X,Y) = 0$. But the converse is in general not true.

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