超球面内任意点的笛卡尔x坐标的密度函数
Probability density function of the Cartesian x-coordinate of the random point inside the hypersphere
摘要：
考虑在以笛卡尔坐标系的原点为中心的n维单位超球面内随机选取的点。这些点的直角坐标是随机变量，它们形成每个点的n维向量。只观察x坐标I，就得到了它的密度函数（PDF）。我表明，它是有关的高斯分布：在限制其同伴PDF？？收敛于标准正态分布的PDF。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
