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Moments of the Distance between Two Random Points
Authors: Narine G. Aharonyan, Victor K. Ohanyan
Number of views: 426
Let D be a bounded convex domain in the Euclidean plane and we choose uniformly and independently points P_(1 )and P_2 from D. Denote by ρ(P_1,P_2 ) the Euclidean distance between points P_(1 )and P_2 and by F_ρ^D (x) the distribution function of ρ(P_1,P_2). Using the explicit form of distribution function we obtain a formula for the calculation of moments of order k for any natural k. In particular, using the formula for F_ρ^D (x), we derive the mean distance between the points P_(1 )and P_2 for a disc, a regular triangle, a rectangle, a regular hexagon and a rhombus (see Santalo, 2004; Burgstaller, Pillichshammer, 2009; Dunbar, 1997).