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An existence theorem for bounds on the expectation of a random variable. Its opportunities for utility theories. V. 2

Harin, Alexander (2015): An existence theorem for bounds on the expectation of a random variable. Its opportunities for utility theories. V. 2.

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Abstract

An existence theorem is proven for the case of a discrete random variable that can take on only a finite set of possible values. If the random variable takes on values in a finite interval and there is a lower non-zero bound on the modulus of (at least one) its central moment, then non-zero bounds on its expectation exist near the borders of the interval. The revealed bounds can be considered as “forbidden zones” for the expectation. They can be useful, e.g., in utility theories.

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