Editing Simplex (section)

=== Probability ===
{{Main|Categorical distribution}}

In probability theory, the points of the standard {{mvar|n}}-simplex in {{math|(''n'' + 1)}}-space form the space of possible probability distributions on a finite set consisting of {{math|''n'' + 1}} possible outcomes. The correspondence is as follows: For each distribution described as an ordered {{math|(''n'' + 1)}}-tuple of probabilities whose sum is (necessarily) 1, we associate the point of the simplex whose [[barycentric coordinates]] are precisely those probabilities. That is, the {{mvar|k}}th vertex of the simplex is assigned to have the {{mvar|k}}th probability of the {{math|(''n'' + 1)}}-tuple as its barycentric coefficient. This correspondence is an affine homeomorphism.