added 1 definition

Author: JoramSoch

D/rvar-uni.md

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+---
+layout: definition
+mathjax: true
+
+author: "Joram Soch"
+affiliation: "BCCN Berlin"
+e_mail: "joram.soch@bccn-berlin.de"
+date: 2020-11-06 03:47:00
+
+title: "Univariate and multivariate random variable"
+chapter: "General Theorems"
+section: "Probability theory"
+topic: "Random variables"
+definition: "Univariate vs. multivariate"
+
+sources:
+  - authors: "Wikipedia"
+    year: 2020
+    title: "Multivariate random variable"
+    in: "Wikipedia, the free encyclopedia"
+    pages: "retrieved on 2020-11-06"
+    url: "https://en.wikipedia.org/wiki/Multivariate_random_variable"
+
+def_id: "D106"
+shortcut: "rvar-uni"
+username: "JoramSoch"
+---
+
+
+**Definition:** Let $X$ be a [random variable](/D/rvar) with possible outcomes $\mathcal{X}$. Then,
+
+* $X$ is called a univariate random variable or [random scalar](/D/rvar), if $\mathcal{X}$ is one-dimensional, i.e. (a subset of) the set of real numbers $\mathbb{R}$;
+
+* $X$ is called a multivariate random variable or [random vector](/D/rvec), if $\mathcal{X}$ is multi-dimensional, e.g. (a subset of) the set of real vectors $\mathbb{R}^n$;
+
+* $X$ is called a matrix-valued random variable or [random matrix](/D/rmat), if $\mathcal{X}$ is (a subset of) the set of real matrices $\mathbb{R}^{n \times p}$.