Probability vector

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.[1]

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 (filled) triangle if , a (filled) tetrahedron , etc.

Properties

See also

References

  1. Jacobs, Konrad (1992), Discrete Stochastics, Basler Lehrbücher [Basel Textbooks], 3, Birkhäuser Verlag, Basel, p. 45, ISBN 3-7643-2591-7, MR 1139766, doi:10.1007/978-3-0348-8645-1.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.