Random variable: Difference between revisions

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==Definition==

A '''random variable''' <math>X</math> is a [[measurable function]] <math>X \colon \Omega \to E</math> from a sample space <math> \Omega </math> as a set of possible [[outcome (probability)|outcome]]s to a [[measurable space]] <math> E</math>. The technical axiomatic definition requires the sample space <math>\Omega</math> to bebelong a sample space ofto a [[probability space|probability triple]] <math>(\Omega, \mathcal{F}, \operatorname{P})</math> (see the [[#Measure-theoretic definition|measure-theoretic definition]]). A random variable is often denoted by capital [[Latin script|Roman letters]] such as <math>X, Y, Z, T</math>.<ref>{{Cite web|title=Random Variables|url=https://www.mathsisfun.com/data/random-variables.html|access-date=2020-08-21|website=www.mathsisfun.com}}</ref>

The probability that <math>X</math> takes on a value in a measurable set <math>S\subseteq E</math> is written as