Distance Between Random Points in Two Rectangular Cities

摘要

The travel distance between two cities of rectangular shape is considered. Two uniformly distributed random points, one from each city, are taken. Their straight path travel distance is then measured. The ecplicit forms for the probability density function of this distance and its expected value are obtained. Numerical results of calculating the exact expected distance and the estimated distance as well as computer simulation are given for various cases. The integer moments of the distance are also discussed.