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

Autor: Pierpaolo Angelini
Jazyk: angličtina
Rok vydání: 2024
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Zdroj: Risks, Vol 12, Iss 1, p 14 (2024)
Druh dokumentu: article
ISSN: 12010014
2227-9091
DOI: 10.3390/risks12010014
Popis: 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 X12 and X12…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.
Databáze: Directory of Open Access Journals
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