Categorical Outcome Variables

Definition

Suppose we have a finite set of outcomes $\Omega $. A categorical outcome variable (or categorical random variable, categorical variable, qualitative variable) is an outcome variable $x: \Omega \to V$ where $V$ is a finite set.

We call $x$ a binary outcome variable (or binary random variable, dichotomous random variable) if $\num{V} = 2$.

Examples

For example, suppose $V = \set{0,1}$. Such an outcome variable is called a Bernoulli random variable.