An Essay on the Prerequisites for the Probability Theory Paolo Rocchi, Mark Burgin

Por • 30 abr, 2022 • Sección: Ambiente

Paolo Rocchi, Mark Burgin

Abstract The probability calculus and statistics as well permeate nearly every discipline and professional sector, while no theories underpinning this wide spreading field reached universal consensus so far. The probability interpretations present irreconcilable traits, so the concept of probability is still substantially unclear. Purpose of this work: The present paper intends to demonstrate how the different models of probability constitute the facial problem which conceals another hidden and more fundamental question. Method: We show how authors do not agree with the concept of probability P and moreover they have different ideas about the precise object qualified by P, which has priority from the point of logic. It is clear how the element X measured by P(X) influences its meaning. In consequence of the conflicting opinions, theorists tend toward a compromise. They use the outcome or result of an experiment as the argument X of P(X) and represent X as a subset of the event space. This paper suggests replacing the outcome-subset with the event-triad E, which provides a comprehensive mathematical support. Results: The last section shows how the triadic model is formally consistent with the conventional theories and can integrate the conflicting views on probability. This unifying result can help mathematicians to go beyond the present theoretical deadlock. In summary, this paper advocates a more explicit notation system for probability and points out how probability can be ambiguous without rigorous specification of the sample space and the experiment in general.

Keywords Probability InterpretationsProbability ArgumentPrimitives of Probability Theory

Share and Cite: Rocchi, P. and Burgin, M. (2020) An Essay on the Prerequisites for the Probability Theory. Advances in Pure Mathematics10, 685-698. doi: 10.4236/apm.2020.1012042.

Paolo Rocchi1,2*Mark Burgin3
1IBM, Roma, Italy.
2LUISS University, Roma, Italy.
3UCLA University, Los Angeles, CA, USA.
DOI: 10.4236/apm.2020.1012042   PDF   HTML   XML   272 Downloads   952 Views

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