Uniform Distribution

A random variable X that assumes the values x₁ , x₂ , .... , x_k has a uniform distribution if it assumes each of the values x₁ , x₂ , .... , x_k with equal probability. The random variable X is said to be uniformly distributed with the following probability mass function:

EX. The random variable X that takes on the value of a single dice roll has a uniform distribution, since X can assume any of the 6 values in the set {1, 2, 3, 4, 5, 6} with an equal probability for each. This probability is 1/6.