Vol. 52, No. 2, 1974

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ISSN: 0030-8730
On the maximum and minimum of partial sums of random variables

Peggy Strait

Vol. 52 (1974), No. 2, 585–593
Abstract

Let X1,X2,,Xn be independent identically distributed random variable with Sk = X1 + X2 + + Xk and Sk+ = max[0,Sk]. We shall derive formulas for the computation of E[min1knSk+],E[max1knSk], and E[min1knSk]. The formulas are then applied to the case of standard normal random variables.

Mathematical Subject Classification 2000
Primary: 60G50
Milestones
Received: 21 February 1973
Revised: 6 June 1973
Published: 1 June 1974
Authors
Peggy Strait