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GAUSSIAN CURVE

Curve studied by de Moivre in 1718 and Gauss in 1809.
Karl Friedrich Gauss (1777 -1855): German astronomer, mathematician, and physicist. Other names: bell curve (of Gauss). |

The area between the curve and the asymptote is equal to |
Cartesian equation: ,
giving the number of individuals of height between x and x
+ dx in a "normal" population of N people, with mean height
m
and a standard deviation s.
For example, the number of subsets with k elements of a set with n elements can be
approximated for large values of n by f(k) with . |

The *Gaussian curve* is the curve of the density
function of the normal
distribution.

For , we get the Gaussian curve said to be "standard".

Do not mistake the bell curve of the Gaussian distribution with that of the Cauchy distribution, which is none other than a witch of Agnesi.

If we break away from the probabilistic aspect, the Gaussian
curve has the following characteristics:

Cartesian equation:
; coordinates of the flex points : .
Area between the curve and the asymptote : ; centroid of this domain : . |

Associated surface of revolution.

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© Robert FERRÉOL 2019