In mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, a degenerate distribution is the probability distribution

Probability distribution

In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....

 of a discrete random variable whose support

Support (mathematics)

In mathematics, the support of a function is the set of points where the function is not zero, or the closure of that set . This concept is used very widely in mathematical analysis...

 consists of only one value. Examples include a two-headed coin and rolling a die whose sides all show the same number. While this distribution does not appear random

Randomness

Randomness has somewhat differing meanings as used in various fields. It also has common meanings which are connected to the notion of predictability of events....

 in the everyday sense of the word, it does satisfy the definition of random variable

Random variable

In probability and statistics, a random variable or stochastic variable is, roughly speaking, a variable whose value results from a measurement on some type of random process. Formally, it is a function from a probability space, typically to the real numbers, which is measurable functionmeasurable...

.

The degenerate distribution is localized at a point k₀ on the real line

Real line

In mathematics, the real line, or real number line is the line whose points are the real numbers. That is, the real line is the set of all real numbers, viewed as a geometric space, namely the Euclidean space of dimension one...

.