Probability vector: Difference between revisions

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Revision as of 14:08, 5 June 2007

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In [[mathematics]] and [[statistics]], a '''probability vector''' or '''stochastic vector''' is a [[vector space|vector]] with non-negative entries that add up to one. Stochastic vectors are commonly used to represent [[discrete probability distribution]]s.

Here are some examples of probability vectors:

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x_3=\begin{bmatrix}0.3 \\ 0.5 \\ 0.07 \\ 0.1 \\ 0.03 \end{bmatrix}.

</math>

Writing out the vector components of a vector <math>p</math> as

:<math>p=\begin{bmatrix} p_1 \\ p_2 \\ \vdots \\ p_n \end{bmatrix}\;</math>

the vector components must sum to one:

:<math>\sum_{i=1}^n p_i = 1</math>

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

:<math>0\le p_i \le 1</math>

for all <math>i</math>. 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.

==See also==

* [[Stochastic matrix]]

{{probability-stub}}

[[Category:Probability theory]]