# cumulative distribution function

(1.1 hours to learn)

## Summary

The cumulative distribution function (CDF) of a random variable X is the function F, where F(a) is the probability that X <= a. CDFs are a convenient representation because they apply to both discrete and continuous random variables, and they can simplify many calculations.

## Context

This concept has the prerequisites:

- random variables (The CDF is a property of a probability distribution.)

## Goals

- Know the definition and basic properties of the CDF

- Be able to use the CDF of a distribution to:
- determine the probability that a random variable lies in a given range
- recover the probability mass function or the probability density function

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

## -Paid-

→ A First Course in Probability

An introductory probability textbook.

- Section 4.2, "Discrete random variables," pages 138-140
- Section 4.9, "Properties of the cumulative distribution function," pages 183-184
- Section 5.1, "Introduction," pages 205-209

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

## -Free-

→ Sets, Counting, and Probability

Online lectures on basic probability theory.

Location:
Lecture "Random variables"

## -Paid-

→ Probability and Statistics

An introductory textbook on probability theory and statistics.

Location:
Section 3.3, "The distribution function," pages 109-116

## See also

-No Additional Notes-