Median

• Definition: Let \(X\) be a continuous random variable with PDF \(f_X\). The median of \(X\) is a point \(c\in\mathbb{R}\) such that

\[\int\limits_{-\infty}^{\infty} f_X(x) \; dx = \int\limits_{c}^{\infty} f_X(x) \; dx\]

• Theorem: The median of a random variable \(X\) is the point \(c\) such that \(F_X(c) = 0.5\).