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Teor. Veroyatnost. i Primenen., 1964, Volume 9, Issue 2, Pages 365–367 (Mi tvp383)  

Short Communications

Über Wahrscheinlichkeit der Aufdeckung des Gebietes bei Linearer Suche

R. S. Guter

Moskau

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
$$ P=\frac{\frac2\pi LV(K)+W(K)}{\pi R^2-L\sqrt{R^2-\frac{L^2}4}-R^2\arcsin\frac L{2R}}. $$
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.

Full text: PDF file (214 kB)

English version:
Theory of Probability and its Applications, 1964, 9:2, 331–333

Bibliographic databases:

Received: 16.07.1962

Citation: R. S. Guter, “Über Wahrscheinlichkeit der Aufdeckung des Gebietes bei Linearer Suche”, Teor. Veroyatnost. i Primenen., 9:2 (1964), 365–367; Theory Probab. Appl., 9:2 (1964), 331–333

Citation in format AMSBIB
\Bibitem{Gut64}
\by R.~S.~Guter
\paper \"Uber Wahrscheinlichkeit der Aufdeckung des Gebietes bei Linearer Suche
\jour Teor. Veroyatnost. i Primenen.
\yr 1964
\vol 9
\issue 2
\pages 365--367
\mathnet{http://mi.mathnet.ru/tvp383}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=163336}
\zmath{https://zbmath.org/?q=an:0132.38803}
\transl
\jour Theory Probab. Appl.
\yr 1964
\vol 9
\issue 2
\pages 331--333
\crossref{https://doi.org/10.1137/1109047}


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