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I have encountered the following problem in my research. As I do not have a strong background in probability theory, I was wondering if anyone here could help me through the following.

I would like to know how one makes rigorous the problem of randomly choosing a unit n-dimensional vector from a uniform distribution.

This is like choosing an point on the n-sphere in which the problem can be solved by switching to generalized spherical coordinates. However, I have read that one can also generate a uniform distribution from a normal distribution of the vector's coorindates, and then dividing by the norm. It is not clear to me why this method produces a uniform distribution.

Thanks Much,

Eric

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# Random Unit Vector From a uniform Distribution

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