What characterizes a Discrete Uniform Probability Distribution?

A Discrete Uniform Probability Distribution is defined by the principle that all outcomes within a specific range have the same probability of occurring. This characteristic ensures that every individual event is equally likely, which is foundational to this type of distribution. As a result, the probability of each outcome can be expressed as a constant value over the range of possible outcomes.

In contrast, distributions where events have different probabilities would not qualify as a uniform distribution, because that would imply a bias towards certain events over others. Similarly, a distribution limited to only two outcomes describes a different scenario known as a Bernoulli distribution, which is not representative of a uniform distribution where several distinct outcomes exist. While discrete uniform distributions do typically deal with whole numbers, this is more a consequence of how the distribution is often applied rather than a defining characteristic. The fundamental criterion remains that all outcomes possess equal probability.