# Machine Learning Encyclopedia

The most well-known measure of similarity between two random variables is the correlation coefficient. Correlation coefficient $\rho between two random variable$X_1$and$X_2 is defined as
$$\rho(X_1,X_2) = \frac{\text{cov}(X_1,X_2)}{\sqrt{\text{var}(X_1), \text{var}(X_2)}}.\nonumber$$
If $X_1$ and $X_2$ are completely correlated, i.e., exact linear dependency exists $\rho(X_1,X_2)$ is $1$ or $-1$. If $X_1$ and $X_2$ are totally uncorrelated, $\rho(X_1,X_2)$ is $0$.