Discrete-Uniform Distribution

The discrete-uniform probability density function is then given by

p_{X} (x) = \frac{1}{N}

for all $x_{i}$ , where $i = 1$ to $N$ for the set of $N$ allowed values of $X$ .

The discrete-uniform distribution function is

F_{X} (x) = \sum_{x \leq x_{i}} p_{X} (x) = \frac{i}{N} .

The discrete-uniform probability density function, as shown in the following figure, is used when a specific set of discrete values are allowed for a random variable, each with equal probability. In the figure below, the allowed values for $X$ are 1, 2, 4, and 8.5.