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The Distribution of the Distance Between Two Random Points in a Convex Set

English

2015
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Russian Journal of Mathematical Research Series A
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English

A formula for calculation of the density function of the distance between two independent points randomly and uniformly chosen in a bounded convex domain D is given. The obtained formula permits to find an explicit form of the density function for the domains D with known chord length distributions. In particular, an application of the formula gives explicit expressions for in the cases of a disc, a regular triangle, a rectangle and a regular pentagon.

doi:10.13187/rjmr.a.2015.1.4
fatcat:ett3ulobhffypbnl5rm4t54r24