Summary
The problem is considered of determining the least upper (or greatest lower) bound for the expected value EK(X 1,…, X n) of a given function K of n random variables X 1, …, X n under the assumption that X 1, …, X n are independent and each X i has given range and satisfies k conditions of the form for i = 1, …, k. It is shown that under general conditions we need consider only discrete random variables X i which take on at most k + 1 values.
This research was supported by the United States Air Force through the Office of Scientific Research of the Air Research and Development Command.
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Hoeffding, W. (1994). The Extrema of the Expected Value of a Function of Independent Random Variables. In: Fisher, N.I., Sen, P.K. (eds) The Collected Works of Wassily Hoeffding. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0865-5_18
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