Correlation

Definition

The correlation between two integrable real-valued random variables with non-zero variance is the quotient of their covariance with the product of their standard deviations.

Two integrable real-valued random variables are uncorrelated if their covariance is zero. We can speak of uncorrelated random variables who have zero variance, although in this case their correlation is undefined.

Notation

Let $f$ and $g$ be two integrable real-valued random variables with $fg$ integrable.