Random Space Filling and Moments of Coverage in Geometrical Probability.

摘要

The moments of the random proportion of a fixed set that is covered by a random set (moments of coverage) are shown to converge under very general conditions to the probability that the fixed set is almost everywhere covered by the random set. Moments and coverage probabilities are calculated for several cases of random arcs of random sizes on a circle. One tends to increase coverage by choosing an arc length distribution that is less peaked at its expectation when that expectation is constrained at a particular value. (Author)