Difference between revisions of "Normal distribution"
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| − | The '''normal distribution''' is | + | {|align="right" border="1" |
| − | The normal probability density function (PDF) is | + | |- |
| + | |<center>probability density function</center> | ||
| + | |- | ||
| + | |[[Image:Norm.png|px=200]] | ||
| + | |- | ||
| + | |<center>cumulative probability function</center> | ||
| + | |- | ||
| + | |[[Image:Law-norm.png|px=200]] | ||
| + | |- | ||
| + | |} | ||
| + | The '''normal distribution''' is a key distribution in the field of [[probability]]. It is also known as the Gaussian distribution, after [[mathematician]] [[Carl Friedrich Gauss|Carl Gauss]], and the [[bell curve]]. | ||
| + | The normal [[probability density function]] (PDF) is | ||
:<math> | :<math> | ||
| − | + | f(x)=\frac{1}{\sqrt{2\pi\sigma^2}} | |
\exp\left[-\frac{1}{2\sigma^2}\left(x-\mu\right)^2\right] | \exp\left[-\frac{1}{2\sigma^2}\left(x-\mu\right)^2\right] | ||
</math> | </math> | ||
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<math>\mu</math> is the [[mean]] and <math>\sigma^2</math> is the [[variance]]. | <math>\mu</math> is the [[mean]] and <math>\sigma^2</math> is the [[variance]]. | ||
| − | [[ | + | If <math>\mu=0</math> and <math>\sigma=1</math>, the distribution is called the ''standard normal distribution'', often denoted by <math>\phi</math>: |
| + | :<math> | ||
| + | \phi(x) = \frac{1}{\sqrt{2\pi}} | ||
| + | \exp(-\frac{1}{2} x^2). | ||
| + | </math> | ||
| + | |||
| + | |||
| + | == See also == | ||
| + | *[[Central limit theorem]] | ||
| + | [[Category:Probability and Statistics]] | ||
Latest revision as of 16:30, July 29, 2016
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The normal distribution is a key distribution in the field of probability. It is also known as the Gaussian distribution, after mathematician Carl Gauss, and the bell curve. The normal probability density function (PDF) is
where
is the mean and 
is the variance.
If 
and 
, the distribution is called the standard normal distribution, often denoted by 
:
