PAIR OF LINES AND MAXIMAL PROBABILITY

Authors

  • A.G. Gasparyan Chair of Probability Theory and Mathematical Statistics, YSU, Armenia

DOI:

https://doi.org/10.46991/PSYU:A/2015.49.2.003

Keywords:

random line, convex domain, translation invariant measure

Abstract

In this paper we consider two independent and identically distributed lines, which intersect a planar convex domain D. We evaluate the probability PD, for the lines to intersect inside D. Translation invariant measures generating random lines is obtained, under which PD 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 PD = p.

Author Biography

A.G. Gasparyan, Chair of Probability Theory and Mathematical Statistics, YSU, Armenia

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Published

2015-06-12

How to Cite

Gasparyan, A. (2015). PAIR OF LINES AND MAXIMAL PROBABILITY. Proceedings of the YSU A: Physical and Mathematical Sciences, 49(2 (237), 3–6. https://doi.org/10.46991/PSYU:A/2015.49.2.003

Issue

Section

Mathematics