\begin{definition}[Definition:Cumulative Distribution Function]
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.
Let $X$ be a real-valued random variable on $\struct {\Omega, \Sigma, \Pr}$.
The '''cumulative distribution function''' (or '''c.d.f.''') of $X$ is denoted $F_X$, and defined as:
:$\forall x \in \R: \map {F_X} x := \map \Pr {X \le x}$
\end{definition}