Moments of the Distance between Two Random Points

Abstract

Let be a bounded convex domain in the Euclidean plane and we choose uniformly and independently points and from Denote by ( ) the Euclidean distance between points and and by ( ) the distribution function of ( ). Using the explicit form of distribution function we obtain a formula for the calculation of moments of order for any natural . In particular, using the formula for ( ), we derive the mean distance between the points and for a disc, a regular triangle, a rectangle, a regular hexagon and a rhombus (see