Probability vector

In mathematics and statistics, a probability vector or stochastic vector is a vector with non-negative entries that add up to one.
The positions (indices) of a probability vector represent the possible outcomes of a discrete random variable, and the vector gives us the probability mass function of that random variable, which is the standard way of characterizing a discrete probability distribution.
Examples.
Here are some examples of probability vectors. The vectors can be either columns or rows.
Geometric interpretation.
Writing out the vector components of a vector formula_5 as
the vector components must sum to one:
Each individual component must have a probability between zero and one:
for all formula_9. Therefore, the set of stochastic vectors coincides with the standard formula_10-simplex. It is a point if formula_11, a segment if formula_12, a (filled) triangle if formula_13, a (filled) tetrahedron formula_14, etc.