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Normal distribution's probability density function derived in 5min

The proof comes from Grossman, Stanley, I., Multivariable Calculus, Linear Algebra, and Differential Equations, 2nd., Academic Press, 1986., and Hamming, Richard, W. The Art of Probability for Engineers and Scientists, Addison-Wesley, 1991. This was summarized by Dan Teague of the North Carolina School of Science and Mathematics. This did not use characteristic functions or moment generating function to derive, because this explanation was straightforward. A disclaimer is that, in the second step, the improper integral appears without proper treatment that this is allowed. However, digging into the details of this would be beyond the scope for this video made to make the content simple.