Probability mass function n=5 where n=b-a+1 Cumulative distribution function n=5 where n=b-a+1. The convention is used that the cumulative mass function is the probability that Parameters   Support Template:Probability distribution/link mass cdf Mean Median Mode N/A Variance Skewness Kurtosis Entropy mgf Char. func. 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 possible values that are equally probable, has a discrete uniform distribution, then the probability of any outcome is . A simple example of the discrete uniform distribution is throwing a fair die. The possible values of are 1, 2, 3, 4, 5, 6; and each time the die 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 where the Heaviside step function is the CDF of the degenerate distribution centered at . 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.

de:Diskrete Gleichverteilung nl:Discrete uniforme verdeling fr:loi uniforme discrète