René's URL Explorer Experiment


Title: Normal Distribution -- from Wolfram MathWorld

Open Graph Title: Normal Distribution -- from Wolfram MathWorld

X Title: Normal Distribution -- from Wolfram MathWorld

Description: A normal distribution in a variate X with mean mu and variance sigma^2 is a statistic distribution with probability density function P(x)=1/(sigmasqrt(2pi))e^(-(x-mu)^2/(2sigma^2)) (1) on the domain x in (-infty,infty). While statisticians and mathematicians uniformly use the term "normal distribution" for this distribution, physicists sometimes call it a Gaussian distribution and, because of its curved flaring shape, social scientists refer to it as the "bell...

Open Graph Description: A normal distribution in a variate X with mean mu and variance sigma^2 is a statistic distribution with probability density function P(x)=1/(sigmasqrt(2pi))e^(-(x-mu)^2/(2sigma^2)) (1) on the domain x in (-infty,infty). While statisticians and mathematicians uniformly use the term "normal distribution" for this distribution, physicists sometimes call it a Gaussian distribution and, because of its curved flaring shape, social scientists refer to it as the "bell...

X Description: A normal distribution in a variate X with mean mu and variance sigma^2 is a statistic distribution with probability density function P(x)=1/(sigmasqrt(2pi))e^(-(x-mu)^2/(2sigma^2)) (1) on the domain x in (-infty,infty). While statisticians and mathematicians uniformly use the term "normal distribution" for this distribution, physicists sometimes call it a Gaussian distribution and, because of its curved flaring shape, social scientists refer to it as the "bell...

Opengraph URL: https://mathworld.wolfram.com/NormalDistribution.html

X: @WolframResearch

direct link

Domain: mathworld.wolfram.com

DC.TitleNormal Distribution
DC.CreatorWeisstein, Eric W.
DC.DescriptionA normal distribution in a variate X with mean mu and variance sigma^2 is a statistic distribution with probability density function P(x)=1/(sigmasqrt(2pi))e^(-(x-mu)^2/(2sigma^2)) (1) on the domain x in (-infty,infty). While statisticians and mathematicians uniformly use the term "normal distribution" for this distribution, physicists sometimes call it a Gaussian distribution and, because of its curved flaring shape, social scientists refer to it as the "bell...
DC.Date.Modified2004-06-24
DC.Subject62E
DC.RightsCopyright 1999-2026 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement.
DC.Formattext/html
DC.Identifierhttps://mathworld.wolfram.com/NormalDistribution.html
DC.Languageen
DC.PublisherWolfram Research, Inc.
DC.Relation.IsPartOfhttps://mathworld.wolfram.com/
DC.TypeText
Last-Modified2004-06-24
og:imagehttps://mathworld.wolfram.com/images/socialmedia/share/ogimage_NormalDistribution.png
og:typewebsite
twitter:cardsummary_large_image
twitter:image:srchttps://mathworld.wolfram.com/images/socialmedia/share/ogimage_NormalDistribution.png
Noneie=edge

Links:

https://www.wolfram.com/mathematica/
https://wolframalpha.com/
https://mathworld.wolfram.com/
https://www.wolfram.com/mathematica/
https://wolframalpha.com/
https://mathworld.wolfram.com/
Algebra https://mathworld.wolfram.com/topics/Algebra.html
Applied Mathematics https://mathworld.wolfram.com/topics/AppliedMathematics.html
Calculus and Analysis https://mathworld.wolfram.com/topics/CalculusandAnalysis.html
Discrete Mathematics https://mathworld.wolfram.com/topics/DiscreteMathematics.html
Foundations of Mathematics https://mathworld.wolfram.com/topics/FoundationsofMathematics.html
Geometry https://mathworld.wolfram.com/topics/Geometry.html
History and Terminology https://mathworld.wolfram.com/topics/HistoryandTerminology.html
Number Theory https://mathworld.wolfram.com/topics/NumberTheory.html
Probability and Statistics https://mathworld.wolfram.com/topics/ProbabilityandStatistics.html
Recreational Mathematics https://mathworld.wolfram.com/topics/RecreationalMathematics.html
Topology https://mathworld.wolfram.com/topics/Topology.html
Alphabetical Index https://mathworld.wolfram.com/letters/
New in MathWorld https://mathworld.wolfram.com/whatsnew/
Probability and Statisticshttps://mathworld.wolfram.com/topics/ProbabilityandStatistics.html
Statistical Distributionshttps://mathworld.wolfram.com/topics/StatisticalDistributions.html
Continuous Distributionshttps://mathworld.wolfram.com/topics/ContinuousDistributions.html
History and Terminologyhttps://mathworld.wolfram.com/topics/HistoryandTerminology.html
Wolfram Language Commandshttps://mathworld.wolfram.com/topics/WolframLanguageCommands.html
Interactive Entrieshttps://mathworld.wolfram.com/topics/InteractiveEntries.html
Click to Copyhttps://mathworld.wolfram.com/topics/ClicktoCopy.html
Download Wolfram Notebookhttps://mathworld.wolfram.com/notebooks/Statistics/NormalDistribution.nb
variatehttps://mathworld.wolfram.com/Variate.html
meanhttps://mathworld.wolfram.com/Mean.html
variancehttps://mathworld.wolfram.com/Variance.html
probability density functionhttps://mathworld.wolfram.com/ProbabilityDensityFunction.html
binomial distributionhttps://mathworld.wolfram.com/BinomialDistribution.html
Wolfram Languagehttp://www.wolfram.com/language/
NormalDistributionhttp://reference.wolfram.com/language/ref/NormalDistribution.html
standard normal distributionhttps://mathworld.wolfram.com/StandardNormalDistribution.html
standard normal distributionhttps://mathworld.wolfram.com/StandardNormalDistribution.html
Fisher-Behrens problemhttps://mathworld.wolfram.com/Fisher-BehrensProblem.html
meanshttps://mathworld.wolfram.com/Mean.html
varianceshttps://mathworld.wolfram.com/Variance.html
normal distribution functionhttps://mathworld.wolfram.com/NormalDistributionFunction.html
erfhttps://mathworld.wolfram.com/Erf.html
erfhttps://mathworld.wolfram.com/Erf.html
root extractionshttps://mathworld.wolfram.com/RootExtraction.html
binomial distributionhttps://mathworld.wolfram.com/BinomialDistribution.html
sample sizehttps://mathworld.wolfram.com/SampleSize.html
meanhttps://mathworld.wolfram.com/Mean.html
variancehttps://mathworld.wolfram.com/Variance.html
distribution functionhttps://mathworld.wolfram.com/DistributionFunction.html
erfhttps://mathworld.wolfram.com/Erf.html
central limit theoremhttps://mathworld.wolfram.com/CentralLimitTheorem.html
meanhttps://mathworld.wolfram.com/Mean.html
meanhttps://mathworld.wolfram.com/Mean.html
variancehttps://mathworld.wolfram.com/Variance.html
normal sum distributionhttps://mathworld.wolfram.com/NormalSumDistribution.html
normal difference distributionhttps://mathworld.wolfram.com/NormalDifferenceDistribution.html
normal ratio distributionhttps://mathworld.wolfram.com/NormalRatioDistribution.html
Cauchy distributionhttps://mathworld.wolfram.com/CauchyDistribution.html
k-statistichttps://mathworld.wolfram.com/k-Statistic.html
unbiased estimatorhttps://mathworld.wolfram.com/UnbiasedEstimator.html
variancehttps://mathworld.wolfram.com/Variance.html
characteristic functionhttps://mathworld.wolfram.com/CharacteristicFunction.html
moment-generating functionhttps://mathworld.wolfram.com/Moment-GeneratingFunction.html
raw momentshttps://mathworld.wolfram.com/RawMoment.html
Gaussian integralshttps://mathworld.wolfram.com/GaussianIntegral.html
central momentshttps://mathworld.wolfram.com/CentralMoment.html
variancehttps://mathworld.wolfram.com/Variance.html
skewnesshttps://mathworld.wolfram.com/Skewness.html
kurtosis excesshttps://mathworld.wolfram.com/KurtosisExcess.html
cumulant-generating functionhttps://mathworld.wolfram.com/Cumulant-GeneratingFunction.html
k-statistichttps://mathworld.wolfram.com/k-Statistic.html
variancehttps://mathworld.wolfram.com/Variance.html
sample variancehttps://mathworld.wolfram.com/SampleVariance.html
uniform distributionhttps://mathworld.wolfram.com/UniformDistribution.html
Box-Muller transformationhttps://mathworld.wolfram.com/Box-MullerTransformation.html
Pearson systemhttps://mathworld.wolfram.com/PearsonSystem.html
chi-squared distributionhttps://mathworld.wolfram.com/Chi-SquaredDistribution.html
68https://mathworld.wolfram.com/NormalDistribution.html#eqn68
chi-squared distributionhttps://mathworld.wolfram.com/Chi-SquaredDistribution.html
gamma distributionhttps://mathworld.wolfram.com/GammaDistribution.html
Binomial Distributionhttps://mathworld.wolfram.com/BinomialDistribution.html
Bivariate Normal Distributionhttps://mathworld.wolfram.com/BivariateNormalDistribution.html
Box-Muller Transformationhttps://mathworld.wolfram.com/Box-MullerTransformation.html
Central Limit Theoremhttps://mathworld.wolfram.com/CentralLimitTheorem.html
Erfhttps://mathworld.wolfram.com/Erf.html
Error Function Distributionhttps://mathworld.wolfram.com/ErrorFunctionDistribution.html
Fisher-Behrens Problemhttps://mathworld.wolfram.com/Fisher-BehrensProblem.html
Galton Boardhttps://mathworld.wolfram.com/GaltonBoard.html
Gaussian Functionhttps://mathworld.wolfram.com/GaussianFunction.html
Half-Normal Distributionhttps://mathworld.wolfram.com/Half-NormalDistribution.html
Inverse Gaussian Distributionhttps://mathworld.wolfram.com/InverseGaussianDistribution.html
Kolmogorov-Smirnov Testhttps://mathworld.wolfram.com/Kolmogorov-SmirnovTest.html
Logit Transformationhttps://mathworld.wolfram.com/LogitTransformation.html
Normal Distribution Functionhttps://mathworld.wolfram.com/NormalDistributionFunction.html
Normal Product Distributionhttps://mathworld.wolfram.com/NormalProductDistribution.html
Normal Ratio Distributionhttps://mathworld.wolfram.com/NormalRatioDistribution.html
Normal Sum Distributionhttps://mathworld.wolfram.com/NormalSumDistribution.html
Owen T-Functionhttps://mathworld.wolfram.com/OwenT-Function.html
Pearson Systemhttps://mathworld.wolfram.com/PearsonSystem.html
Ratio Distributionhttps://mathworld.wolfram.com/RatioDistribution.html
Standard Normal Distributionhttps://mathworld.wolfram.com/StandardNormalDistribution.html
Tetrachoric Functionhttps://mathworld.wolfram.com/TetrachoricFunction.html
z-Scorehttps://mathworld.wolfram.com/z-Score.html
Explore this topic in the MathWorld classroomhttps://mathworld.wolfram.com/classroom/NormalDistribution.html
normal distribution https://www.wolframalpha.com/input/?i=normal+distribution
normal distribution table https://www.wolframalpha.com/input/?i=normal+distribution+table
plot normal distribution sigma=1 mu=0 https://www.wolframalpha.com/input/?i=plot+normal+distribution+sigma%3D1+mu%3D0
CRC Standard Mathematical Tables, 28th ed.http://www.amazon.com/exec/obidos/ASIN/1584882913/ref=nosim/ericstreasuretro
An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd ed.http://www.amazon.com/exec/obidos/ASIN/0471257087/ref=nosim/ericstreasuretro
An Introduction to Probability Theory and Its Applications, Vol. 2, 3rd ed.http://www.amazon.com/exec/obidos/ASIN/0471257095/ref=nosim/ericstreasuretro
Gamma: Exploring Euler's Constant.http://www.amazon.com/exec/obidos/ASIN/0691099839/ref=nosim/ericstreasuretro
Mathematics of Statistics, Pt. 2, 2nd ed.http://www.amazon.com/exec/obidos/ASIN/B0007HR7SY/ref=nosim/ericstreasuretro
Mathematical Recreations.http://www.amazon.com/exec/obidos/ASIN/0486201635/ref=nosim/ericstreasuretro
Probability, Random Variables, and Stochastic Processes, 2nd ed.http://www.amazon.com/exec/obidos/ASIN/0070484686/ref=nosim/ericstreasuretro
Handbook of the Normal Distribution.http://www.amazon.com/exec/obidos/ASIN/0824793420/ref=nosim/ericstreasuretro
Theory and Problems of Probability and Statistics.http://www.amazon.com/exec/obidos/ASIN/0070602816/ref=nosim/ericstreasuretro
Mathematical Snapshots, 3rd ed.http://www.amazon.com/exec/obidos/ASIN/0486409147/ref=nosim/ericstreasuretro
The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed.http://www.amazon.com/exec/obidos/ASIN/B0006BP2CE/ref=nosim/ericstreasuretro
Normal Distributionhttps://www.wolframalpha.com/input/?i=normal+distribution
Weisstein, Eric W.https://mathworld.wolfram.com/about/author.html
MathWorldhttps://mathworld.wolfram.com/
https://mathworld.wolfram.com/NormalDistribution.htmlhttps://mathworld.wolfram.com/NormalDistribution.html
Probability and Statisticshttps://mathworld.wolfram.com/topics/ProbabilityandStatistics.html
Statistical Distributionshttps://mathworld.wolfram.com/topics/StatisticalDistributions.html
Continuous Distributionshttps://mathworld.wolfram.com/topics/ContinuousDistributions.html
History and Terminologyhttps://mathworld.wolfram.com/topics/HistoryandTerminology.html
Wolfram Language Commandshttps://mathworld.wolfram.com/topics/WolframLanguageCommands.html
Interactive Entrieshttps://mathworld.wolfram.com/topics/InteractiveEntries.html
Click to Copyhttps://mathworld.wolfram.com/topics/ClicktoCopy.html
About MathWorldhttps://mathworld.wolfram.com/about/
MathWorld Classroomhttps://mathworld.wolfram.com/classroom/
Contributehttps://mathworld.wolfram.com/contact/
MathWorld Bookhttps://www.amazon.com/exec/obidos/ASIN/1420072218/ref=nosim/weisstein-20
wolfram.comhttps://www.wolfram.com
13,439 Entrieshttps://mathworld.wolfram.com/whatsnew/
Last Updated: Mon Jul 6 2026https://mathworld.wolfram.com/whatsnew/
©1999–2026 Wolfram Research, Inc.https://www.wolfram.com
Terms of Usehttps://www.wolfram.com/legal/terms/mathworld.html
https://www.wolfram.com
wolfram.comhttps://www.wolfram.com
Wolfram for Educationhttps://www.wolfram.com/education/

Viewport: width=device-width, initial-scale=1


URLs of crawlers that visited me.