Probability density function of the Cartesian x-coordinate of the random point inside the hypersphere
Statistics Theory
2013-06-04 v1 Statistics Theory
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.
Keywords
Cite
@article{arxiv.1306.0290,
title = {Probability density function of the Cartesian x-coordinate of the random point inside the hypersphere},
author = {Argyn Kuketayev},
journal= {arXiv preprint arXiv:1306.0290},
year = {2013}
}
Comments
7 pages, 3 figures