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 p as the vector components must sum to one: Each individual component must have a probability between zero and one: for all i. Therefore, the set of stochastic vectors coincides with the standard (n-1)-simplex. It is a point if n=1, a segment if n=2, a (filled) triangle if n=3, a (filled) tetrahedron if n=4, etc.

Properties