Definition:Random Variable/Definition 2

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Definition

Let $\EE$ be an experiment with a probability space $\struct {\Omega, \Sigma, \Pr}$.

A random variable on $\struct {\Omega, \Sigma, \Pr}$ is a mapping $X: \Omega \to \R$ such that:

$\forall x \in \R: \set {\omega \in \Omega: \map X \omega \le x} \in \Sigma$


The image $\Img X$ of $X$ is often denoted $\Omega_X$.


Also see


Sources