Moments of the Random Proportion of an Arc Which Is in the Shadows Cast by Randomly Located Disks of Random Size.

摘要

The present paper is devoted to the study of some properties of the distribution of the total portion of an arc length which is under shadow. The total portion of an arc which is under shadow (or under light) is a random variable having a distribution which is determined by the stochastic properties of the shadow casting objects. In the present Technical Report we show how the moments of this distribution can be determined. Explicit formulas are given for the expection and variance of the total portion in the light, or any specified arc on the circumference of the circle. Preliminary results on the actual distribution are available, but will be provided in a different paper. (Author)