A distribution in which a discrete random variable, X, say, can take a discrete set of possible values x1, x2,…, xn, with equal probabilities, so that Often the set of possible values is the set of positive integers 1, 2,…, n, and in this case the mean is and the variance is .
As an example, the score on a single throw of an unbiased die has a uniform discrete distribution on 1, 2, 3, 4, 5, 6, with mean 7/2 and variance 35/12.