\begin{definition}[Definition:Laplace Distribution]
Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.
Let $\Img X = \R$. 
Let $\mu$ be a real number. 
Let $b$ be a strictly positive real number.
$X$ is said to have a '''Laplace distribution''' with parameters $\mu$ and $b$ {{iff}} it has probability density function:
:$\map {f_X} x = \dfrac 1 {2 b} \map \exp {- \dfrac {\size {x - \mu} } b}$
This is written: 
:$X \sim \map {\operatorname {Laplace} } {\mu, b}$
\end{definition}