On the Probability of Detecting a Region by a Linear Search

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1964 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:Theory of Probability & Its Applications, volume 9, pages 331-333 (issn: 0040-585X, eissn: 1095-7219,

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Authors: Guter, R. S.;

doi: 10.1137/1109047

On the Probability of Detecting a Region by a Linear Search

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Abstract

Lying in a circle G is a convex rectifiable region K. If a cut L is made in the circle at random then the probability of cutting the region K is \[ P = \frac{{\frac{2}{\pi }LV(K) + W(K)}}{{\pi R^2 - L\sqrt {R^2 - \frac{{L^2 }}{4}} - R^2 \arcsin \frac{L}{{2R}}}}. \] Here, $V(K)$ and $W(K)$ are the linear and planar variations of K in the sense of A. S. Kronrod and A. G. Vitushkin.

Keywords

probability theory, convex rectifiable region in circle, probability of region cutting, Geometric probability and stochastic geometry, linear search, linear random cut

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