\begin{definition}[Definition:Log Normal Distribution]
Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.
Let $\Img X = \R_{>0}$.
$X$ is said to have a '''log normal distribution''' {{iff}} it has probability density function: 
:$\ds \map {f_X} x = \dfrac 1 {\sigma \sqrt {2 \pi} x } \map \exp {-\dfrac {\paren {\map \ln x - \mu}^2} {2 \sigma^2} }$
for $\mu \in \R, \sigma \in \R_{> 0}$.
\end{definition}