Journal of Prime Research in Mathematics

# On random covering of a circle

$$^{1}$$Corresponding Author: naeemtazkeer@yahoo.com
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 $$S_n$$.