On certain characterization of normal distribution

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Abstract

A conjecture of Bobkov and Houdré (1995), recently proved by Kwapień et al. (1995), stated that if X and Y are symmetric i.i.d. real random variables such that P(|(X + Y)/√2| > t) ⩽ P(|X| > t) for any t > 0, then X has normal distribution. In this note, we give some generalization of their result with a short and simple proof which can be useful in some other cases.

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Cited by (3)

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Supported in part by Foundation for Polish Science and KBN Grant 2 P301 022 07.

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