Definition:Median of Continuous Random Variable

Definition
Let $X$ be a continuous random variable on a probability space $\left({\Omega, \Sigma, \Pr}\right)$.

Let $X$ have probability density function $f_X$.

A median of $X$ is defined as a real number $m_X$ such that:


 * $\displaystyle \operatorname{Pr} \left({X < \mu}\right) = \int_{-\infty}^{m_X} f_X \left({x}\right) \rd x = \frac 1 2$