random variable

A random variable assigns a value to the outcome of an experiment.

Formally,
a random variable is a measurable function $X:\mathrm{\Omega }\to R$ from the sample space $\mathrm{\Omega }$ equipped with event space $\mathcal{F}$ to a measurable space $(R,\mathcal{R})$.

$X(\omega )=r$ means that $X:\omega \mapsto r$ maps outcome $\omega \in \mathrm{\Omega }$ to value $r\in R$.

Typically, $R$ is the set of real numbers $\mathbb{R}$; in general, $X$ is an $R$-valued random variable.