# independent events

(1.4 hours to learn)

## Summary

Intuitively, two events are independent if the first event happening doesn't influence whether the second is likely to occur. Mathematically, some set of events are independent if the joint probability of some subset of the events decomposes into a product of the probabilities of the individual events. In statistics and AI, a probabilistic model often must make independence assumptions in order for things to be efficiently computable.

## Context

This concept has the prerequisites:

- probability (Independence is a property of events in a probability space.)
- conditional probability (The definition of independence can be thought of in terms of conditional probability.)

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

## -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.

## -Paid-

→ Mathematical Statistics and Data Analysis

An undergraduate statistics textbook.

Location:
Section 1.6, "Independence," pages 23-26

→ An Introduction to Probability Theory and its Applications

A classic introductory probability textbook.

Location:
Section 5.3, "Stochastic independence," pages 114-117

→ Probability and Statistics

An introductory textbook on probability theory and statistics.

Location:
Section 2.2, "Independent events," pages 56-64

→ A First Course in Probability

An introductory probability textbook.

Location:
Section 3.4, "Independent events," pages 87-101

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

## -Free-

→ BerkeleyX: Introduction to Statistics: Probability

→ Sets, Counting, and Probability

Online lectures on basic probability theory.

Location:
Lecture sequence "Conditional probability"

→ Khan Academy: Probability and Statistics

## See also

- This notion of independence can be extended to random variables .
- Independence can also be characterized in terms of conditional distributions .