Definition: Random variable

Index: The Book of Statistical Proofs ▷ General Theorems ▷ Probability theory ▷ Random variables ▷ Random variable

Definition: A random variable may be understood

• informally, as a real number $X \in \mathbb{R}$ whose value is the outcome of a random experiment;

• formally, as a measurable function $X$ defined on a probability space $(\Omega, \mathcal{E}, P)$ that maps from a sample space $\Omega$ to the real numbers $\mathbb{R}$ using an event space $\mathcal{E}$ and a probability function $P$;

• more broadly, as any random quantity $X$ such as a random event, a random scalar, a random vector or a random matrix.

 

Sources:

• Wikipedia (2020): "Random variable"; in: Wikipedia, the free encyclopedia, retrieved on 2020-05-27; URL: https://en.wikipedia.org/wiki/Random_variable#Definition.

Metadata: ID: D65 | shortcut: rvar | author: JoramSoch | date: 2020-05-27, 22:36.