On the expected range and expected adjusted range of partial sums of exchangeable random variables

Studies of storage capacity of reservoirs, under the assumption of infinite storage, lead to the problem of finding the distribution of the range or adjusted range of partial sums of random variables. In this paper, formulas for the expected values of the range and adjusted range of partial sums of exchangeable random variables are presented. Such formulas are based on an elegant result given in Spitzer (1956). Some consequences of the aforementioned formulas are discussed.