Discrete uniform distribution

A probability distribution that assigns the same probability to every outcome in a finite set. For a set of n outcomes, each has probability 1/n.

Probability mass function: A function that assigns a probability to each possible value of a discrete random variable. It expresses the distribution by assigning probability 1/n to each allowed value.
Expected value: The probability-weighted average of a random variable's possible values. For equally likely numeric values, the expected value is their ordinary arithmetic mean.
Fair die: A die whose faces have equal probabilities of landing upward in a roll. A standard fair die is a six-outcome example, assigning probability 1/6 to each face.
Discrete probability distribution: A probability distribution over a finite or countably infinite set of values. Discrete uniform distributions are the equal-probability special case of this broader family.
Sample space: The set of all possible outcomes of a random experiment. The distribution is uniform when every outcome in its finite sample space is equally likely.
Variance: The expected squared distance of a random variable from its mean. Equal probabilities make its variance a scaled sum of squared deviations across the support.
Random number generation: The production of values according to a specified random or pseudorandom process. Uniform integer generators aim to select each value in a finite range with equal probability.
Categorical distribution: A distribution over a finite set of categories that may assign different probabilities to each category. Unlike the uniform case, a categorical distribution permits unequal category probabilities.
Equally likely outcomes: Outcomes that have the same probability of occurring. Equality of outcome probabilities is the defining condition for this distribution.
Bernoulli trial: A random experiment with two outcomes, conventionally labeled success and failure. A Bernoulli variable has only two possible values, while uniform distributions can span larger finite sets.

Linked from 3 pages

Bernoulli distributionCompared with: It matches Bernoulli only when both outcomes have probability one-half.