added 1 definition

Author: JoramSoch

D/rvar-disc.md

@@ -0,0 +1,34 @@
+---
+layout: definition
+mathjax: true
+
+author: "Joram Soch"
+affiliation: "BCCN Berlin"
+e_mail: "joram.soch@bccn-berlin.de"
+date: 2020-10-29 04:44:00
+
+title: "Discrete and continuous random variable"
+chapter: "General Theorems"
+section: "Probability theory"
+topic: "Random variables"
+definition: "Discrete vs. continuous"
+
+sources:
+  - authors: "Wikipedia"
+    year: 2020
+    title: "Random variable"
+    in: "Wikipedia, the free encyclopedia"
+    pages: "retrieved on 2020-10-29"
+    url: "https://en.wikipedia.org/wiki/Random_variable#Standard_case"
+
+def_id: "D105"
+shortcut: "rvar-disc"
+username: "JoramSoch"
+---
+
+
+**Definition:** Let $X$ be a [random variable](/D/rvar) with possible outcomes $\mathcal{X}$. Then,
+
+* $X$ is called a discrete random variable, if $\mathcal{X}$ is either a finite set or a countably infinite set; in this case, $X$ can be described by a [probability mass function](/D/pmf);
+
+* $X$ is called a continuous random variable, if $\mathcal{X}$ is an uncountably infinite set; if it is absolutely continuous, $X$ can be described by a [probability density function](/D/pdf).