In mathematics, the discrete uniform distribution are probability distributions 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 x₁, x₂, ..., x_n that are equally probable has a discrete uniform distribution, then the probability of any outcome x_i is 1/n. A simple example of the discrete uniform distribution is throwing a fair die. The possible values of x 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, is possible to express the cumulative distribution function in terms of the degenerate distribution, thus

where the Heaviside step function θ(x) is the CDF of the degenerate distribution at x = 0.