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 Post subject: Random unit vectors in n-spacePosted: Fri, 17 Jun 2011 16:25:40 UTC
 S.O.S. Oldtimer

Joined: Thu, 13 Jul 2006 19:47:54 UTC
Posts: 308
Let V be the set of vectors in s.t. under the standard norm. Let be random vectors which are outcomes from a uniform distribution on V. What is the probability that the angle between v_1 and v_2 is less than a given angle ?

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 Post subject: Re: Random unit vectors in n-spacePosted: Fri, 17 Jun 2011 16:55:19 UTC
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Zathras wrote:
Let V be the set of vectors in s.t. under the standard norm. Let be random vectors which are outcomes from a uniform distribution on V. What is the probability that the angle between v_1 and v_2 is less than a given angle ?

Think of this as fixing and choosing a random , so it is just computation of the volume of ball of radius in the geometry , which is

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