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.

If a random variable has any of n possible values k_1,k_2,…,k_n that are equally probable, then it has a discrete uniform distribution. The probability of any outcome ki is 1/n. A simple example of the discrete uniform distribution is throwing a fair die. The possible values of k are 1, 2, 3, 4, 5, 6; and each time the die is thrown, the probability of a given score is 1/6.

The probability mass function of the discrete uniform distribution is:

f(x,a,b) =   

1/(b-a+1) for a⇐x⇐b   

0 otherwise

support a ⇐ x ⇐ b