Some Asymptotic Results for a Coverage Problem

line at random, without overlap. 2. The given path length is placed at random on the long line. Some related experimental work has been done [1], with photomicrographs of sections on solid Boron Carbide-Zirconium mixtures. In this work a number of linear paths of fixed length and parallel to one axis of the photograph were taken at positions along the other axis of the photograph and the length of Boron Carbide covered by each path was measured. It is interesting to note that the frequency of zero fraction intercept predicted by the idealization was in good agreement with experimental results. The small differences found were in the direction suggested by the fact that the sampled line had to be of finite thickness. That is, the predicted frequency of zero intercept tended to be slightly higher than observed. 2. Assumptions and Summary of Results. We assume we have a sample of line segments A1, A2, X , * * An which are independent random drawings from a universe of segments with probability density p(A), 0 nAM. We call a configuration admissible if