Steele, J. Michael2023-05-232023-05-232016-01-012017-08-18https://repository.upenn.edu/handle/20.500.14332/48104The Bruss-Robertson inequality gives a bound on themaximal number of elements of a random sample whose sum is less than a specifiedvalue, and the extension of that inequality which is given hereneither requires the independence of the summands nor requires the equality of their marginal distributions. A review is also given of the applications of the Bruss-Robertson inequality,especially the applications to problems of combinatorial optimization such as the sequential knapsack problem and the sequential monotone subsequence selection problem.This work is licensed under a Creative Commons Attribution 3.0 License.Order statistical inequalitiessequential knapsack problemsequential monotone subsequence problemsequential selectiononline selectionMarkov decision problemsresource dependent branching processesBellman equationPhysical Sciences and MathematicsArticle