Uniform0a
Uniform0a is a discrete, finite uniform distribution defined on the set of integers {0, 1, ..., a}, where a is a nonnegative integer. In this convention each value in the range has equal probability, namely P(X = k) = 1/(a + 1) for k = 0, 1, ..., a. Uniform0a is a discrete analogue of the continuous Uniform(0, a) distribution and is sometimes used in contexts where a finite, equally likely set of outcomes is required.
Definition and notation: For each integer a ≥ 0, a random variable X is said to follow Uniform0a
Moments and distribution properties: The mean is E[X] = a/2, and the variance is Var(X) = a(a + 2)/12.
Relations and limits: Uniform0a is a special case of the discrete uniform distribution on a finite set.
Applications: It is used in simple randomized algorithms, combinatorial modeling, hashing, and simulations where a finite,