# covariance

(1.4 hours to learn)

## Summary

The covariance of two random variables is a measure of their relatedness. It is closely related to the correlation coefficient, but is more commonly used in probability theory because it has nice mathematical properties.

## Context

This concept has the prerequisites:

## Goals

• Know the definitions of covariance and correlation
• Write the covariance in terms of the moments of the distribution
• Know the Cauchy-Schwartz inequality for covariance (which bounds the covariance in terms of the individual variances)
• Be able to compute the variance of a linear combination of random variables in terms of their variances and covariances
• Know that independent random variables have zero covariance
• Show that variance of a sum of independent random variables is a sum of the variances

## -Free-

Mathematical Monk: Probability Primer (2011)
Online videos on probability theory.
Other notes:
• This uses the measure theoretic notion of probability, but should still be accessible without that background. Refer to Lecture 1.S for unfamiliar terms.