
Proceedings of the Yerevan State University, series Physical and Mathematical Sciences, 2015, Issue 2, Pages 3–6
(Mi uzeru17)




This article is cited in 1 scientific paper (total in 1 paper)
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.
Received: 11.05.2015 Accepted: 29.05.2015
Citation:
A. G. Gasparyan, “Pair of lines and maximal probability”, Proceedings of the YSU, Physical and Mathematical Sciences, 2015, no. 2, 3–6
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