Derivation of the Normal (Gaussian) Distribution

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Published at : 11 Jan 2021
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In this video, I'll derive the formula for the normal/Gaussian distribution. This argument is adapted from the work of the astronomer John Herschel in 1850 and the physicist James Clerk Maxwell in 1860.

A similar argument is presented in this video: https://www.youtube.com/watch?v=ebewBjZmZTw&t=224s

References / Further Reading:
1. The Evolution of the Normal Distribution: http://www.ww.ingeniousmathstat.org/sites/default/files/pdf/upload_library/22/Allendoerfer/stahl96.pdf

2. The Central Gaussian, or Normal, Distribution: http://www-biba.inrialpes.fr/Jaynes/cc07s.pdf

3. J.C. Maxwell "Illustrations of the Dynamical Theory of Gases" (p. 152-154): http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Maxwell_1860_Equilibrium_distribution.pdf

4. https://en.wikipedia.org/wiki/Gaussian_integral

5. https://en.wikipedia.org/wiki/Functional_equation

Erratum:
32:35 - the left-hand side should be positive, not negative.
Bell curveNormal DistributionGaussian

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