Probability vector: Difference between revisions

Revision as of 17:27, 30 November 2010

Revision as of 20:06, 24 March 2011

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===Some Properties of <math>n</math> dimensional Probability Vectors===

: Probability vectors of dimension <math>n</math> are contained within an <math>n-1</math> dimensional unit [[hyperspherehyperplane]].

: The mean of a probability vector is <math> 1/n </math>.

: The shortest probability vector has the value <math> 1/n </math> as each component of the vector, and has a length of <math>1/\sqrt n</math>.

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: No two probability vectors in the <math>n</math> dimensional unit hypersphere are collinear unless they are identical.

: The length of a probability vector is equal to <math>\sqrt {n\sigma^2 + 1/n} </math>; where <math> \sigma^2 </math> is the variance of the elements of the probability vector.

==See also==

* [[Stochastic matrix]]