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arXiv · 1306.0290

Probability density function of the Cartesian x-coordinate of the random point inside the hypersphere

Argyn Kuketayev
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Abstract

Consider randomly picked points inside the n-dimensional unit hypersphere centered at the origin of the Cartesian coordinate system. The Cartesian coordinates of the points are random variables, which form an n-dimensional vector for each point. Observing only the x-coordinate I obtained its probability density function (PDF). I show that it is related to the Gaussian distribution: in limit its companion PDF?? converges to the PDF of the standard normal distribution.

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Argyn Kuketayev. 2013-06-03. Probability density function of the Cartesian x-coordinate of the random point inside the hypersphere. https://arxiv.org/abs/1306.0290

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