Definition:Pearson Correlation Coefficient

Definition
Let $X$ and $Y$ be random variables.

Let the variances of $X$ and $Y$ exist and be finite.

Then the Pearson correlation coefficient of $X$ and $Y$, typically denoted $\map \rho {X, Y}$, is defined by:


 * $\map \rho {X, Y} = \dfrac {\cov {X, Y} } {\sqrt {\var X \, \var Y} }$

where $\cov {X, Y}$ is the covariance of $X$ and $Y$.