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Forbidden zones for the expectation of a random variable. New version 1

Harin, Alexander (2018): Forbidden zones for the expectation of a random variable. New version 1.

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A forbidden zones theorem is deduced in the present article. Its consequences and applications are preliminary considered. The following statement is proven: if some non-zero lower bound exists for the variance of a random variable, that takes on values in a finite interval, then non-zero bounds or forbidden zones exist for its expectation near the boundaries of the interval. The article is motivated by the need of rigorous theoretical support for the practical analysis that has been performed for the influence of scattering and noise in the behavioral economics, decision sciences, utility and prospect theories. If a noise can be one of possible causes of the above lower bound on the variance, then it can cause or broaden out such forbidden zones. So the theorem can provide new possibilities for mathematical description of the influence of such a noise. The considered forbidden zones can evidently lead to some biases in measurements.

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