\begin{definition}[Definition:Exponential Distribution]
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Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.
Then $X$ has the '''exponential distribution with parameter $\beta$''' {{iff}}:
:$\map X \Omega = \R_{\ge 0}$
:$\map \Pr {X < x} = 1 - e^{-\frac x \beta}$
where $0 < \beta$.
It is written:
:$X \sim \Exponential \beta$
\end{definition}