Definition:Cumulative Distribution Function

Definition
Let $\left({\Omega, \Sigma, \Pr}\right)$ be a probability space.

Let $X$ be a random variable on $\left({\Omega, \Sigma, \Pr}\right)$.

The cumulative distribution function (or c.d.f.) of $X$ is denoted $F \left({X}\right)$, and defined as:
 * $\forall x \in \R: F \left({X}\right) \left({x}\right) := \Pr \left({X \le x}\right)$

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.

Also see

 * Survival Function, a closely related concept


 * Properties of Cumulative Distribution Function