Gauss$504851$ - translation to English
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Gauss$504851$ - translation to English

WIKIMEDIA DISAMBIGUATION PAGE
Gauss-markov; Gauss-Markov; Gauss–Markov (disambiguation); Gauss-Markov (disambiguation)

Gauss      
n. Gauss familienaam; Karl Friedrich Gauss (1777-1855), Duits wiskundige en wetenschapper die belangrijkste bijdrage leverde aan de cijfertheorie en elektromagnetische theorie
Carl Friedrich Gauss         
  • heliotrope]] (background: mathematical signs) and a section of the [[triangulation network]]
  • German 10-[[Deutsche Mark]] [[Banknote]] (1993; discontinued) with formula and graph of normal distribution (background: some Göttingen buildings); portrait as mirror image of the Jensen portrait
  • Lithography by [[Siegfried Bendixen]] (1828)
  • Brunswick]]
  • House of birth in Brunswick (destroyed in World War II)
  • German Research Centre for Geosciences]] in [[Potsdam]]
  • Gauss on his deathbed (1855)
  • [[Copley Medal]] for Gauss (1838)
  • Caricature of Abraham Gotthelf Kästner by Gauss (1795)
  • Carl Friedrich Gauß 1803 by Johann Christian August Schwartz
  • Title page of Gauss' magnum opus, ''[[Disquisitiones Arithmeticae]]''
  • [[Gauss's diary]] entry related to sum of triangular numbers (1796)
  • Portrait of Gauss in Volume II of "''Carl Friedrich Gauss Werke''," 1876
  • Title page of ''Intensitas vis Magneticae Terrestris ad Mensuram Absolutam Revocata''
  • Title page of ''Theoria Motus Corporum Coelestium in sectionibus conicis solem ambientium''
  • Title page to the English Translation of ''Theoria Motus'' by [[Charles Henry Davis]] (1857)
  • Parochial registration]] of Gauss' birth
  • [[Survey marker]] stone in Garlste (now [[Garlstedt]])
  • Old observatory (circa 1800)
  • Albani Cemetery]] in [[Göttingen]], Germany
  • Gauss-Weber monument in Göttingen
  • Gauss' second wife Wilhelmine Waldeck
  • Ludwig Becker]]
GERMAN MATHEMATICIAN AND PHYSICIST (1777–1855)
Johann Carl Friedrich Gauss; Karl Gauss; Carl Frederich Gauss; Karl Friedrich Gauss; Carl Gauss; C. F. Gauss; Carl F. Gauss; Carl Friedrich Gauß; Johann Friedrich Karl Gauss; C.F. Gauss; Carl friedrich gauss; Carl Friederich Gauss; C. F. Gauß; Guass; CF Gauss; Karl Friedrich Gauß; Carl Freidrich Gauss; Johann Carl Friedrich Gauß; Carl Gauß; Friedrich gauss; Gauss; Johann Karl Friedrich Gauss; Carolus Fridericus Gauss; Princeps mathematicorum; Religious views of Carl Friedrich Gauss; Gauß, Johann Carl Friedrich; Carl Friedrich Gausz
Carl Friedrich Gauss (1777-1855), Duitse wiskundige en natuurkundige die veel bijgedragen heeft aan cijferleer voor kansberekening en voor onderzoek van elektro-magnetische velden
normal distribution         
  • [[Carl Friedrich Gauss]] discovered the normal distribution in 1809 as a way to rationalize the [[method of least squares]].
  • As the number of discrete events increases, the function begins to resemble a normal distribution
  • Comparison of probability density functions, <math>p(k)</math> for the sum of <math>n</math> fair 6-sided dice to show their convergence to a normal distribution with increasing <math>na</math>, in accordance to the central limit theorem. In the bottom-right graph, smoothed profiles of the previous graphs are rescaled, superimposed and compared with a normal distribution (black curve).
  • Histogram of sepal widths for ''Iris versicolor'' from Fisher's [[Iris flower data set]], with superimposed best-fitting normal distribution.
  • Fitted cumulative normal distribution to October rainfalls, see [[distribution fitting]]
  • [[Pierre-Simon Laplace]] proved the [[central limit theorem]] in 1810, consolidating the importance of the normal distribution in statistics.
  • The [[bean machine]], a device invented by [[Francis Galton]], can be called the first generator of normal random variables. This machine consists of a vertical board with interleaved rows of pins. Small balls are dropped from the top and then bounce randomly left or right as they hit the pins. The balls are collected into bins at the bottom and settle down into a pattern resembling the Gaussian curve.
  • '''a:''' Probability density of a function <math>\cos x^2</math> of a normal variable <math>x</math> with <math>\mu=-2</math> and <math>\sigma=3</math>. '''b:''' Probability density of a function <math>x^y</math> of two normal variables <math>x</math> and <math>y</math>, where <math>\mu_x=1</math>, <math>\mu_y=2</math>, <math>\sigma_x = 0.1</math>, <math>\sigma_y = 0.2</math>, and <math>\rho_{xy} = 0.8</math>. '''c:''' Heat map of the joint probability density of two functions of two correlated normal variables <math>x</math> and <math>y</math>, where <math>\mu_x = -2</math>, <math>\mu_y=5</math>, <math>\sigma_x^2 = 10</math>, <math>\sigma_y^2 = 20</math>, and <math>\rho_{xy} = 0.495</math>. '''d:''' Probability density of a function <math display="inline">\sum_{i=1}^4 \vert x_i \vert</math> of 4 iid standard normal variables. These are computed by the numerical method of ray-tracing.<ref name="Das" />
  • The ground state of a [[quantum harmonic oscillator]] has the [[Gaussian distribution]].
  • For the normal distribution, the values less than one standard deviation away from the mean account for 68.27% of the set; while two standard deviations from the mean account for 95.45%; and three standard deviations account for 99.73%.
PROBABILITY DISTRIBUTION
Bell Curve; Gaussian distribution; NormalDistribution; Normal Distribution; Standard normal distribution; Law of error; Cumulative normal; Normally distributed; Cumulative Normal distribution; Normality (statistics); Standard normal; Normal density function; Normal curve; Normal distribution curve; Normal Curve; Normal random variable; The bell-shaped curve; Gaussian normal distribution; Gaussian Distributions; Gaussian Distribution; Bell-shaped; Gaussian random variable; Error Distribution; Bell-shaped curve; Standard distribution; Error distribution; Bell-curve; Normal distributions; Bell distribution; Normal probability distribution; Gaussian density; Gauss distribution; Normal cumulative distribution function; Bell Curves; Bell curves; Normal distribution about the mean; Gaussian probability density function; Gaussian probability distribution; Normal Model; Standard normal random variable; Gaussian profile; Normal-distribution; Bell-shaped frequency distribution curve; Gaussian distributions; Normal distribution quantile function; E-x2; E−x2; Normal population; Cumulative distribution function of the normal distribution; Bellcurve; Univariate Gaussian; Univariate Gaussian distribution; Bell curve; Bell shaped curve; Operations on normal deviates; Operations on normal distributions; Normal deviate; Standard normally distributed; Approximately normal distribution; Normalcdf; Gaussian pdf; Normal density; Normaldist
normale distributie (gelijke verdeling in klokdiagram weergegeven)

Definition

Carl Friedrich Gauss
<person> A German mathematician (1777 - 1855), one of all time greatest. Gauss discovered the method of least squares and Gaussian elimination. Gauss was something of a child prodigy; the most commonly told story relates that when he was 10 his teacher, wanting a rest, told his class to add up all the numbers from 1 to 100. Gauss did it in seconds, having noticed that 1+...+100 = 100+...+1 = (101+...+101)/2. He did important work in almost every area of mathematics. Such eclecticism is probably impossible today, since further progress in most areas of mathematics requires much hard background study. Some idea of the range of his work can be obtained by noting the many mathematical terms with "Gauss" in their names. E.g. Gaussian elimination (linear algebra); Gaussian primes (number theory); Gaussian distribution (statistics); Gauss [unit] (electromagnetism); Gaussian curvature (differential geometry); Gaussian quadrature (numerical analysis); Gauss-Bonnet formula (differential geometry); {Gauss's identity} (hypergeometric functions); Gauss sums ({number theory}). His favourite area of mathematics was number theory. He conjectured the Prime Number Theorem, pioneered the {theory of quadratic forms}, proved the {quadratic reciprocity theorem}, and much more. He was "the first mathematician to use complex numbers in a really confident and scientific way" (Hardy & Wright, chapter 12). He nearly went into architecture rather than mathematics; what decided him on mathematics was his proof, at age 18, of the startling theorem that a regular N-sided polygon can be constructed with ruler and compasses if and only if N is a power of 2 times a product of distinct Fermat primes. (1995-04-10)
Show more definitions

Wikipedia

Gauss–Markov

The phrase Gauss–Markov is used in two different ways:

  • Gauss–Markov processes in probability theory
  • The Gauss–Markov theorem in mathematical statistics (in this theorem, one does not assume the probability distributions are Gaussian.)
https://en.wikipedia.org/wiki/Gauss–Markov
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