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

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

Risks, 2024, vol. 12, issue 1, 1-17

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.

Keywords: probability spaces; function of estimation; two-valued logic; ?-product; many-valued logic; multilinear measure (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2024
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