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Invariance of the Mathematical Expectation of a Random Quantity and Its Consequences

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  • Pierpaolo Angelini

    (Dipartimento di Scienze Statistiche, Università La Sapienza, Piazzale Aldo Moro 5, 00185 Roma, Italy)

Abstract

Possibility and probability are the two aspects of uncertainty, where uncertainty represents the ignorance of a given individual. The notion of alternative (or event) belongs to the domain of possibility. An event is intrinsically subdivisible and a quadratic metric, whose value is intrinsic or invariant, is used to study it. By subdividing the notion of alternative, a joint (bivariate) distribution of mass appears. The mathematical expectation of X is proved to be invariant using joint distributions of mass. The same is true for X 12 and X 12 … m . This paper describes the notion of α -product, which refers to joint distributions of mass, as a way to connect the concept of probability with multilinear matters that can be treated through statistical inference. This multilinear approach is a meaningful innovation with regard to the current literature. Linear spaces over R with a different dimension can be used as elements of probability spaces. In this study, a more general expression for a measure of variability referred to a single random quantity is obtained. This multilinear measure is obtained using different joint distributions of mass, which are all considered together.

Suggested Citation

  • Pierpaolo Angelini, 2024. "Invariance of the Mathematical Expectation of a Random Quantity and Its Consequences," Risks, MDPI, vol. 12(1), pages 1-17, January.
    • Handle: RePEc:gam:jrisks:v:12:y:2024:i:1:p:14-:d:1321768
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    References listed on IDEAS

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