This may serve as an alternative definition of discrete random variables.

Categorical distribution: for discrete random variables with a finite set of values.

Consider the transformation from a continuum to a discrete variable:

In this sense, it is the strongest way to measure the information content of a discrete random variable.

Often only such discrete variables are called "quantized"; usage varies.

Let be a discrete random variable that takes values 1,2,.

The difference between the results for discrete and continuous variables may surprise many readers.

(This idea can be generalized to discrete variables with more than two possible values.)

The members of a special ordered set individually may be continuous or discrete variables in any combination.

They may be continuous or discrete ordinal variables like counts.