Definition: Discrete and continuous random variable
Index: The Book of Statistical Proofs ▷ General Theorems ▷ Probability theory ▷ Random variables ▷ Discrete vs. continuous
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Metadata: ID: D105  shortcut: rvardisc  author: JoramSoch  date: 20201029, 04:44.
Definition: Let $X$ be a random variable 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;

$X$ 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.
 Wikipedia (2020): "Random variable"; in: Wikipedia, the free encyclopedia, retrieved on 20201029; URL: https://en.wikipedia.org/wiki/Random_variable#Standard_case.
Metadata: ID: D105  shortcut: rvardisc  author: JoramSoch  date: 20201029, 04:44.