This content is licensed under Creative Commons Attribution/Share-Alike License 3.0 (Unported). That means you may freely redistribute or modify this content under the same license conditions and must attribute the original author by placing a hyperlink from your site to this work https://planetcalc.com/8125/. Also, please do not modify any references to the original work (if any) contained in this content.
Covariance between two discrete random variables
where E(X) is the mean of X, and E(Y) is the mean of Y.
Note that we only know sample means for both variables, that's why we have n-1 in the denominator
If the covariance is positive, then increasing one variable results in the increase of another variable. If the covariance is negative, then increasing one variable results in the decrease of another variable. The absolute value of covariance is usually normalized by dividing by the product of the variables' standard deviations. This is the so-called Pearson correlation coefficient.