Let X1,X2,...,Xn be independent random variables with a fixed, common parent distribution for which the p-th moment EℝXℝp is defined. Then the maximum order statistic XÅ(nÅ) grows at a rate that is o(n1’/p) in expectation, in probability and a.e. Explicit bounds of this order can be given for EXÅ(nÅ) in terms of the moments of X. Thus the expectation of the extreme grows slowly with the sample size. This observation is applied to the speed-up realized by parallel computation, and to the performance of scheduling policies.
