Discrete probability distribution
Discrete Uniform distribution
X ~ DiscreteUniform(a, b)
Every integer from a to b is equally likely. It models perfectly fair, finite outcomes and underlies fair dice and random integer selection.
Explore it interactivelyKey facts
- Notation
- X ~ DiscreteUniform(a, b)
- Type
- discrete
- Parameters
- a, b — smallest and largest integer values
- Support
- {a, a+1, …, b}, with n = b − a + 1 values
- PMF
- P(X = k) = 1 / n, for each integer a ≤ k ≤ b
- Mean
- (a + b) / 2
- Variance
- (n² − 1) / 12
When to use it
- Rolling a fair die
- Picking a random integer in a range
- A fair lottery draw
Related distributions
Frequently asked questions
What is the Discrete Uniform distribution?
Every integer from a to b is equally likely. It models perfectly fair, finite outcomes and underlies fair dice and random integer selection.
What are the mean and variance of the Discrete Uniform distribution?
For X ~ DiscreteUniform(a, b), the mean is (a + b) / 2 and the variance is (n² − 1) / 12.
When is the Discrete Uniform distribution used?
It is commonly used for: Rolling a fair die; Picking a random integer in a range; A fair lottery draw.