Do probabilities and Statistics belong to Physics or Mathematics


Authors : Dr. Ismail Abbas

Volume/Issue : Volume 8 - 2023, Issue 1 - January

Google Scholar : https://bit.ly/3IIfn9N

Scribd : https://bit.ly/3ICc5rX

DOI : https://doi.org/10.5281/zenodo.7645209

In general, probability and statistics are a missing part of mathematics and belong to physics rather than mathematics. In previous papers we have shown that the solution of partial differential equations such as Laplace's and Poisson's PDE with Dirichlet boundary conditions and the time-dependent heat equation in its most general form can be solved via the physical chains of matrix B. Moreover, we have also shown that numerical statistical integration and differentiation can be performed via the same statistical numerical method called Cairo technique. In this paper, we extend the above work and apply the B matrix to rigorously derive the well-known normal/Gaussian statistical distribution. In other words, we show that the law of Normal/Gaussian Distribution belongs to physics rather than mathematics. We present numerical results for two arbitrary special cases without loss of generality. The processing and precision of the numerical results of the new unconventional technique for the derivation and application process are striking, and its robustness is beyond doubt. We also clarify that although the classical Gaussian mathematical law and the proposed Gaussian physical statistical law have exactly the same formula, they are completely different in their nature and concepts and therefore in the way of sampling judgment and applications.

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