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 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 as
the vector components must sum to one:
Each individual component must have a probability between zero and one:
for all. Therefore, the set of stochastic vectors coincides with the standard -simplex. It is a point if, a segment if, a triangle if, a tetrahedron, etc.

Properties