# Uniform Discrete Probability Distribution Family

A Uniform Discrete Probability Distribution Family is a discrete probability distribution family that is a uniform probability distribution family composed of uniform discrete probability functions.

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

## References

### 2015

- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Uniform_distribution_(discrete) Retrieved:2015-6-22.
- 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 an integer interval

*[a,b]*, so that*a,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]\displaystyle{ F(k;a,b)=\frac{\lfloor k \rfloor -a + 1}{b-a+1} }[/math]

- In probability theory and statistics, the '