Probability density distribution of random line segments inside a convex body: Application to random media

We study the probability density distribution of random line segments entirely contained inside a convex body of R-n. Relations between this distribution function and other distribution functions of importance in geometric probability are shown. The expression for the probability density distribution of random line segments is given for several simple geometric bodies in R-2, R-3, and R-n, application to random media is then presented. (C) 2003 American Institute of Physics.