How do you DERIVE the BELL CURVE?

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:    • Normal distribution's probability den...  

References / Further Reading:
1. The Evolution of the Normal Distribution: http://www.ww.ingeniousmathstat.org/s...

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

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

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

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

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