History of the Normal Distribution - University of Utah

History of the Normal

Distribution

Jenny Kenkel

History of the Normal Distribution

Jenny Kenkel November 8th, 2016

Probabiltiy Distributions

History of the Normal

Distribution

Jenny Kenkel

A probability distribution is a function f (x) so that

b

P(a < X < b) = f (x)dx

a

The Normal Distribution

History of the Normal

Distribution

Jenny Kenkel

The normal distribution is a family of distributions, given by

1 f (x) =

e-

(x -?)2 22

22

The Standard Normal has ? = 0 and = 1, i.e.

1 x2 f (x) = e 2

2

Changing ? changes the location of the curve, and changing changes the spread of the curve

Arbuthnot: "An argument for Divine Providence, taken from the constant Regularity observ'd in the Births of both Sexes"

History of the Normal

Distribution

Jenny Kenkel

Argued the probability

that more males than

females were born every

year from 1629 to 1710,

82 years, was

1 82 2

Arbuthnot: "An argument for Divine Providence, taken from the constant Regularity observ'd in the Births of both Sexes"

History of the Normal

Distribution

Jenny Kenkel

Argued the probability

that more males than

females were born every

year from 1629 to 1710,

82 years, was

1 82 2

But the fact that not

many more males than

females were born every

year was proof polygamy is

contrary to the laws of

nature

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