TY - JOUR
AU - Gasparyan, A.G.
PY - 2015/06/12
Y2 - 2024/08/16
TI - PAIR OF LINES AND MAXIMAL PROBABILITY
JF - Proceedings of the YSU A: Physical and Mathematical Sciences
JA - Proc. YSU A: Phys. Math. Sci.
VL - 49
IS - 2 (237)
SE - Mathematics
DO - 10.46991/PSYU:A/2015.49.2.003
UR - https://journals.ysu.am/index.php/proceedings-phys-math/article/view/vol49_no2_2015_pp003-006
SP - 3-6
AB - <p>In this paper we consider two independent and identically distributed lines, which intersect a planar convex domain <strong>D</strong>. We evaluate the probability <em>P</em><strong><sub>D</sub></strong>, for the lines to intersect inside <strong>D</strong>. Translation invariant measures generating random lines is obtained, under which <em>P</em><strong><sub>D</sub></strong> achieves its maximum for a disc and a rectangle. It is also shown that for every <em>p</em> from the interval [0,1/2] and for every square there are measures generating random lines such that <em>P</em><strong><sub>D</sub></strong> = <em>p</em>.</p>
ER -