Authors :
Dr. Ismail Abbas
Volume/Issue :
Volume 8 - 2023, Issue 3 - March
Google Scholar :
https://bit.ly/3TmGbDi
Scribd :
https://tinyurl.com/2yrkyms8
DOI :
https://doi.org/10.5281/zenodo.8328088
Abstract :
In particular, probability and statistics are a
missing part of mathematics and classical theoretical
physics.
The introduction of the stochastic transition matrix
B proposed by the Cairo Physical Technique suggests
that probability and statistics should belong to physics
rather than mathematics.
We first study the comparison between chains of
stochastic Markov transitions (mathematics) and chains
of B transition matrices (physics) as a clear approach to
elucidate this subject and better understand both from
the point of view of probability by definition and
limitation of application.
The in-depth study shows that the B-matrix chains
originally introduced to solve the general case of the
time-dependent diffusion equation can also find
numerical integration formulas, numerically derive the
normal/Gaussian distribution, and find the numerical
values of the Gamma function in the positive x domain.
The numerical results presented are surprisingly
accurate and validate the B transition matrix hypothesis.
In particular, probability and statistics are a
missing part of mathematics and classical theoretical
physics.
The introduction of the stochastic transition matrix
B proposed by the Cairo Physical Technique suggests
that probability and statistics should belong to physics
rather than mathematics.
We first study the comparison between chains of
stochastic Markov transitions (mathematics) and chains
of B transition matrices (physics) as a clear approach to
elucidate this subject and better understand both from
the point of view of probability by definition and
limitation of application.
The in-depth study shows that the B-matrix chains
originally introduced to solve the general case of the
time-dependent diffusion equation can also find
numerical integration formulas, numerically derive the
normal/Gaussian distribution, and find the numerical
values of the Gamma function in the positive x domain.
The numerical results presented are surprisingly
accurate and validate the B transition matrix hypothesis.
