# Uniform Probability Mass Function

A Uniform Probability Mass Function is a discrete probability function that is a uniform probability function.

**AKA:**Discrete Uniform Probability Function.**Context:**- It can (typically) be from a Finite Support Discrete Probability Distribution Family.

**Example(s):**- the Probability Function associated with a Fair Coin Toss Experiment.

**Counter-Example(s):****See:**Symmetric Distribution, Cumulative Distribution Function, Finite Support Discrete Probability Distribution Family.

## References

### 2017

- (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Discrete_uniform_distribution Retrieved:2017-7-16.
- In probability theory and statistics, the
**discrete uniform distribution**is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of*n*values has equal probability 1/*n*. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by all integers in an interval [

*a*,*b*], so that*a*and*b*become the main parameters of the distribution (often one simply considers the interval [1,*n*] with the single parameter*n*). With these conventions, the cumulative distribution function (CDF) of the discrete uniform distribution can be expressed, for any*k*∈ [*a*,*b*], as : [math] F(k;a,b)=\frac{\lfloor k \rfloor -a + 1}{b-a+1} [/math]

- In probability theory and statistics, the

### 2011

- (IS, 2014) ⇒ http://www.introductorystatistics.com/escout/main/Glossary.htm Retrieved:2011-11-06
- Equally likely outcomes A theoretical probability model, such as that for a fair die, in which every outcome has the same probability; also called discrete uniform