{n(1-e^t)}\,| char =$\backslash frac\{e^\{iat\}-e^\{i(b+1)t\}\}\{n(1-e^\{it\})\}\backslash ,$| }}

In probability theory and statistics, the discrete uniform distribution is a discrete probability distribution that can be characterized by saying that all values of a finite set of possible values are equally probable.

A random variable that has any of $n$ possible values $k\_1,k\_2,\backslash dots,k\_n$ that are equally probable, has a discrete uniform distribution, then the probability of any outcome $k\_i$  is $1/n$. A simple example of the discrete uniform distribution is throwing a fair dice. The possible values of $k$ are 1, 2, 3, 4, 5, 6; and each time the dice is thrown, the probability of a given score is 1/6.

In case the values of a random variable with a discrete uniform distribution are real, it is possible to express the cumulative distribution function in terms of the degenerate distribution; thus

$F(k;a,b,n)=\{1\backslash over\; n\}\backslash sum\_\{i=1\}^n\; H(k-k\_i)$

where the Heaviside step function $H(x-x\_0)$ is the CDF of the degenerate distribution centered at $x\_0$. This assumes that consistent conventions are used at the transition points.

See rencontres numbers for an account of the probability distribution of the number of fixed points of a uniformly distributed random permutation.

Discrete distributions

Rovnoměrné rozdělení (diskrétní) | Diskrete Gleichverteilung | Loi uniforme discrète | Variabile casuale Uniforme discreta | Discrete uniforme verdeling | Дискретное равномерное распределение