# What is a distribution function?

#### Understand the Problem

The question is asking about the concept of a distribution function, which is commonly used in statistics and probability theory to describe the probability distribution of a random variable. It typically involves understanding how probabilities are assigned to the possible outcomes of a random variable.

#### Answer

A distribution function gives the probability that a random variable is ≤ a specific value.

A distribution function (often called a cumulative distribution function or CDF) is a mathematical expression that provides the probability that a random variable is less than or equal to a specific value.

##### Answer for screen readers

A distribution function (often called a cumulative distribution function or CDF) is a mathematical expression that provides the probability that a random variable is less than or equal to a specific value.

#### More Information

Distribution functions play a crucial role in probability theory and statistics as they allow the characterization of random variables and their associated probabilities.

#### Tips

Confusing a distribution function with a probability density function (PDF) is common. The CDF gives the probability up to a certain value, while a PDF gives the probability density at a specific value.

#### Sources

- Distribution function - Wikipedia - en.wikipedia.org
- Distribution Function -- from Wolfram MathWorld - mathworld.wolfram.com
- Distribution function | Probability, Density & Variance - Britannica - britannica.com