\begin{definition}[Definition:Median of Continuous Random Variable]
Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.
Let $X$ have probability density function $f_X$. 
A '''median''' of $X$ is defined as a real number $m_X$ such that: 
:$\ds \map \Pr {X < m_X} = \int_{-\infty}^{m_X} \map {f_X} x \rd x = \frac 1 2$
\end{definition}