Editing Joint probability distribution (section)

=== Correlation ===
{{Main|Correlation}}

There is another measure of the relationship between two random variables that is often easier to interpret than the covariance.

The correlation just scales the covariance by the product of the standard deviation of each variable. Consequently, the correlation is a dimensionless quantity that can be used to compare the linear relationships between pairs of variables in different units. If the points in the joint probability distribution of X and Y that receive positive probability tend to fall along a line of positive (or negative) slope, ρ<sub>XY</sub> is near +1 (or −1). If ρ<sub>XY</sub> equals +1 or −1, it can be shown that the points in the joint probability distribution that receive positive probability fall exactly along a straight line. Two random variables with nonzero correlation are said to be correlated. Similar to covariance, the correlation is a measure of the linear relationship between random variables.

The correlation coefficient between the random variables <math>X</math> and <math>Y</math> is
:<math>\rho_{XY}=\frac{\operatorname{cov}(X,Y)}{\sqrt{V(X)V(Y)}}=\frac{\sigma_{XY}}{\sigma_X\sigma_Y}.</math>