Journal of Prime Research in Mathematics
Vol. 1 (2008), Issue 1, pp. 127 – 131
ISSN: 1817-3462 (Online) 1818-5495 (Print)
ISSN: 1817-3462 (Online) 1818-5495 (Print)
On random covering of a circle
Muhammad Naeem
Faculty of Engineering Sciences. GIK Institute. TOPI (SWABI), Pakistan.
\(^{1}\)Corresponding Author: naeemtazkeer@yahoo.com
Copyright © 2008 Muhammad Naeem. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Published: December, 2008.
Abstract
Let \(X_{j}\), \(j = 1, 2, …, n\) be the independent and identically distributed random vectors which take the values on the unit circumference. Let \(S_{n}\) be the area of the convex polygon having \(X_{j}\) as vertices. The paper by Nagaev and Goldfield (1989) has proved the asymptotic normality of random variableSn. Our main aim is to show that the random variableSn can be represented as a sum of functions of uniform spacings. This allows us to apply known results related to uniform spacings for the analysis of \(S_n\).