When all outcomes in a sample space have the same probability of occurring, the sample space is referred to as a uniform distribution. In a uniform distribution, each event or outcome is equally likely to happen.
For example, if you roll a fair six-sided die, the sample space consists of six outcomes (1, 2, 3, 4, 5, and 6), and since the die is fair, the probability of each outcome is \( \frac{1}{6} \).
Uniform distributions can apply to both discrete and continuous random variables. In a discrete uniform distribution, all outcomes are distinct and finite, while in a continuous uniform distribution, outcomes are spread evenly over an interval.