Distribution of the Distance between Two Random Points in a Body from R~3

摘要

In the present paper a formula for calculation of the density function f(rho)(x) of the distance between two independent points randomly and uniformly chosen in a bounded convex body D is given. The formula permits to find an explicit form of density function f(rho)(x) for body D with known chord length distributions. In particular, we obtain an explicit expression for f(rho)(x) in the case of a ball of diameter d in R-3.