A discrete uniform random variable is a discrete random variable for which the probability of each outcome is the same.
Example
The roll of a die is a discrete uniform random variable and has a discrete uniform probability distribution.
The random variable X can take the values X = {1, 2, 3, 4, 5, 6}
Each outcome has a probability of 1/6.
The probability distribution and cumulative distribution functions are shown below:
| xi | Probability distribution, P(xi) | Cumulative Distribution, F(xi) |
| 1 | 1/6 | 1/6 = 0.1667 |
| 2 | 1/6 | 2/6 = 0.333 |
| 3 | 1/6 | 3/6 = 0.5 |
| 4 | 1/6 | 4/6 = 0.667 |
| 5 | 1/6 | 5/6 = 0.833 |
| 6 | 1/6 | 6/6 = 1 |
Let’s observe a few values from the above table.
P(3) = 1/6 or 0.1667
F(3) = 0.5
P(2<=X<=5) = 4\*1/6 = 0.667We can generalize this as follows:
P(x) = 1/6 or 0.1667
Cumulative distribution function for any outcome i is F(xi) = i\*P(x)
Probability function for a range with k outcomes = k\*P(x)