ON THE RANGE OF PARTIAL SUMS OF A FINITE NUMBER OF INDEPENDENT NORMAL VARIATES

Abstract

The properties of the range of the partial sums S1, S1, …, Sn of the independent variates X1, X2 …, Xn, are important in the theory of storage capacity. The asymptotic distribution, for large n, is known (Feller, 1951). The present paper discusses the mean value of the range for finite n, in the case where the X1 are standard normal variates. This is shown to depend on the integral