Inmathematics and statistics, a probability vectororstochastic 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.[1]
Here are some examples of probability vectors. The vectors can be either columns or rows.
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 (filled) triangle if , a (filled) tetrahedron , etc.