# independent random variables

(1.1 hours to learn)

## Summary

Intuitively, two random variables are independent if they don't influence each other. Mathematically, two random variables are independent if the events associated with each random variable lying in some set are independent. In statistics and probabilistic modeling, different random variables are often assumed to be independent in order to allow for efficient estimation and inference.

## Context

This concept has the prerequisites:

## Core resources (read/watch one of the following)

## -Free-

→ Mathematical Monk: Probability Primer (2011)

Online videos on probability theory.

Additional dependencies:

- expectation and variance

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.

## -Paid-

→ A First Course in Probability

An introductory probability textbook.

Location:
Section 6.2, "Independent random variables," pages 267-279

→ Mathematical Statistics and Data Analysis

An undergraduate statistics textbook.

Location:
Section 3.4, "Independent random variables," pages 84-86

→ Probability and Statistics

An introductory textbook on probability theory and statistics.

Location:
Section 3.5, "Marginal distributions," subsection "Independent random variables," pages 131-135

## Supplemental resources (the following are optional, but you may find them useful)

## -Free-

→ Sets, Counting, and Probability

## See also

- We may also want to ask whether two variables are independent conditioned on a third .