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discrete uniform
Probability mass function
Discrete uniform probability mass function for n=5
n=5 where n=b-a+1
Cumulative distribution function
Discrete uniform cumulative mass function for n=5
n=5 where n=b-a+1. The convention is used that the cumulative mass function is the probability that

Template:Probability distribution/link mass
Mode N/A
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.

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