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 Proceedings of the YSU, Physical and Mathematical Sciences, 2015, Issue 2, Pages 3–6 (Mi uzeru17)

Mathematics

Pair of lines and maximal probability

A. G. Gasparyan

Yerevan State University

Abstract: In this paper we consider two independent and identically distributed lines, which intersect a planar convex domain $\mathbf{D}.$ We evaluate the probability $P_ { \mathbf{D}},$ for the lines to intersect inside $\mathbf{D}$.
Translation invariant measures generating random lines is obtained, under which $P_ {\mathbf{D}}$ achieves its maximum for a disc and a rectangle. It is also shown that for every $p$ from the interval $[0, 1/2]$ and for every square there are measures generating random lines such that $P_ { \mathbf{D}}=p.$

Keywords: random line, convex domain, translation invariant measure.

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MSC: Primary 60D05; Secondary 52A22; 53C65
Accepted:29.05.2015
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Citation: A. G. Gasparyan, “Pair of lines and maximal probability”, Proceedings of the YSU, Physical and Mathematical Sciences, 2015, no. 2, 3–6

Citation in format AMSBIB
\Bibitem{Gas15} \by A.~G.~Gasparyan \paper Pair of lines and maximal probability \jour Proceedings of the YSU, Physical and Mathematical Sciences \yr 2015 \issue 2 \pages 3--6 \mathnet{http://mi.mathnet.ru/uzeru17} 

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This publication is cited in the following articles:
1. A. G. Gasparyan, Orientation dependent chord length distribution and covariogram for bounded convex bodies, Abstract of dissertation submitted for the degree of candidate of phys-math sciences Specialty: A.01.05 "Probability theory and mathematical statistics", Yerevan, 2016, 17 pp.
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