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MA181 INTRODUCTION TO STATISTICAL MODELLING
NORMAL DISTRIBUTION
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DIAGRAMS
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\item[Origins]
The normal distribution was discovered, in a discrete form, by de
Moivre in 1733 as an approximation to the binomial distribution.
It was later shown, in 1812, to be the limiting distribution of a
sample mean by Laplace. Meanwhile, in 1809, Gauss derived the
normal as the distribution of errors in astronomical observations.
\item[Formulation]
Let $Y$ be a random variable with the probability density function
(pdf)
$$f(y)=\frac{1}{\sigma\sqrt{2\pi}}\exp\left[-\frac{(y-\mu)^2}{2\sigma^2}\right],\
-\infty