# Definition:Cumulative Distribution Function

## Definition

Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.

Let $X$ be a random variable on $\struct {\Omega, \Sigma, \Pr}$.

The cumulative distribution function (or c.d.f.) of $X$ is denoted $\map F X$, and defined as:

$\forall x \in \R: \map {\map F X} x := \map \Pr {X \le x}$

## Also known as

Some sources refer to this as a distribution function, but it can then become confused with the concept of a distribution function in physics.