Random copy of a segment within a convex domain |
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Authors: | N G Aharonyan H S Harutyunyan V K Ohanyan |
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Institution: | 1.Department of Mathematics and Mechanics,Yerevan State University,Yerevan,Armenia |
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Abstract: | Under the assumption that S is a segment of the length l and D is a bounded, convex domain in the Euclidean plane ℝ2, the paper considers the randomly moving copy L of S, under the condition that it hits D. Denote by L| the length of L ∩ D. In the paper an elementary expression for the distribution function F
L
(x) of the random variable L| is obtained. Note that F
L
(x) can have a jump at the point l or can be a continuous function depending on l and the domainD. In particular, a relation between chord length distribution functions of D and F
L
(x) is given. Moreover, we derive explicit forms of F
L
(x) for the disk and regular n-gons with n = 3÷7. |
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Keywords: | |
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