69.243.144.129 at 03:36, 12 December 2014

2014-12-12T03:36:58Z

en>Jack Greenmaven: Reverted 1 edit by 190.147.173.12 identified as test/vandalism using STiki

2013-11-25T20:06:25Z

Reverted 1 edit by 190.147.173.12 identified as test/vandalism using STiki

← Older revision		Revision as of 22:06, 25 November 2013
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	~~Adrianne is what you has the capability to call me but Which~~ [~~http://www.google.co.uk/search?hl=en&gl=us&tbm=nws&q=i+don%27t&gs_l=news i don't~~] ~~like when guys and women use my full logo~~. ~~What I take great delight in doing is~~ [~~http://mondediplo.com/spip~~.~~php?page=recherche&recherche=fish+preventing fish preventing] and I~~'~~ll be opening up something else along to barefoot jogging. Filing is probably my day job now but soon I~~'ll be very on my own. Vermont displays always been my livelihood place and I are blessed with everything that I have to have here. Go to some of my website to find competeing more: http://prometeu.net<br><br>		''[[Stochastic vector]] redirects here. For the concept of a random vector, see [[Multivariate random variable]].''

	~~my blog post~~: ~~clash~~ of ~~clans cheats (~~[~~http~~://~~prometeu~~.~~net http~~://~~prometeu~~.~~net~~])		{{Unreferenced\|date=December 2009}}
			In [[mathematics]] and [[statistics]], a '''probability vector''' or '''stochastic vector''' is a [[vector space\|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. The vectors can be either columns or rows.

			<math>
			x_0=\begin{bmatrix}0.5 \\ 0.25 \\ 0.25 \end{bmatrix},\;

			x_1=\begin{bmatrix} 0 \\ 1 \\ 0 \end{bmatrix},\;

			x_2=\begin{bmatrix} 0.65 & 0.35 \end{bmatrix},\;

			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}\quad \text{or} \quad p=\begin{bmatrix} p_1 & p_2 & \cdots & 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.

			==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 [[hyperplane]].
			: 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>.
			: The longest probability vector has the value 1 in a single component and 0 in all others, and has a length of 1.
			: The shortest vector corresponds to maximum uncertainty, the longest to maximum certainty.
			: 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]]

			{{DEFAULTSORT:Probability Vector}}
			[[Category:Probability theory]]
			[[Category:Vectors]]

en>I dream of horses: Reverted edit(s) by 42.241.119.203 identified as test/vandalism using STiki;

2012-08-15T18:49:18Z

Reverted edit(s) by 42.241.119.203 identified as test/vandalism using STiki;

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Adrianne is what you has the capability to call me but Which [http://www.google.co.uk/search?hl=en&gl=us&tbm=nws&q=i+don%27t&gs_l=news i don't] like when guys and women use my full logo. What I take great delight in doing is [http://mondediplo.com/spip.php?page=recherche&recherche=fish+preventing fish preventing] and I'll be opening up something else along to barefoot jogging. Filing is probably my day job now but soon I'll be very on my own. Vermont displays always been my livelihood place and I are blessed with everything that I have to have here. Go to some of my website to find competeing more: http://prometeu.net<br><br>

my blog post: clash of clans cheats ([http://prometeu.net http://prometeu.net])

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69.243.144.129 at 03:36, 12 December 2014

en>Jack Greenmaven: Reverted 1 edit by 190.147.173.12 identified as test/vandalism using STiki

en>I dream of horses: Reverted edit(s) by 42.241.119.203 identified as test/vandalism using STiki;