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arXiv · 1204.1633

Self-Inverse and Exchangeable Random Variables

Theophilos Cacoullos·Nickos Papadatos
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Abstract

A random variable Z will be called self-inverse if it has the same distribution as its reciprocal 1/Z. It is shown that if Z is defined as a ratio, X/Y, of two rv's X and Y (with Pr[X=0]=Pr[Y=0]=0), then Z is self-inverse if and only if X and Y are (or can be chosen to be) exchangeable. In general, however, there may not exist iid X and Y in the ratio representation of Z.

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Theophilos Cacoullos, Nickos Papadatos. 2012-06-29. Self-Inverse and Exchangeable Random Variables. https://doi.org/10.1016/j.spl.2012.06.032

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