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
Abstract :
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.
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.
