Continuous Support of a Random Variable

Last updated Nov 1, 2022

Let $(\Omega, \mathcal{B}, \mathbb{P})$ be a Probability Space and let $X: \Omega \to \mathbb{R}^{n}$ be a Continuous Random Variable with Probability Density Function $f_{X} : \mathbb{R}^{n} \to \mathbb{R}{\geq 0}$. Then the support of $X$ is $$\text{supp} X = {y \in \mathbb{R} : f{X}(y) > 0}$$