PAIR OF LINES AND MAXIMAL PROBABILITY
DOI:
https://doi.org/10.46991/PSYU:A/2015.49.2.003Keywords:
random line, convex domain, translation invariant measureAbstract
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.
Downloads
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
License
Copyright (c) 2015 Proceedings of the YSU
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.