*Stochastic vector redirects here. For the concept of a random vector, see Multivariate random variable.*

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.

Here are some examples of probability vectors:

Writing out the vector components of a vector as

the vector components must sum to one:

One also has the requirement that each individual component must have a probability between zero and one:

for all . These two requirements show that stochastic vectors have a geometric interpretation: A stochastic vector is a point on the "far face" of a standard orthogonal simplex. That is, a stochastic vector uniquely identifies a point on the face opposite of the orthogonal corner of the standard simplex.

Read more about Probability Vector: Some Properties of Dimensional Probability Vectors

### Famous quotes containing the word probability:

“Only in Britain could it be thought a defect to be “too clever by half.” The *probability* is that too many people are too stupid by three-quarters.”

—John Major (b. 1943)