Normal Distribution: Difference between revisions
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Bradley Monk (talk | contribs) (Created page with "The normal distribution is :<math> f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{ -\frac{(x-\mu)^2}{2\sigma^2} }. </math> The parameter ''μ'' in this formula is the ''mean'' or ''exp...") |
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The normal distribution is | The normal distribution is | ||
f(x) | <big><big> | ||
</ | f(x) {{=}} (<sup>1</sup>⁄<sub>σ √2π </sub>) e<sup>-(<sup>(x-µ)<sup>2</sup></sup> ⁄ <sub>2σ<sup>2</sup></sub>)</sup> | ||
</big></big> | |||
The parameter ''μ'' in this formula is the ''mean'' or ''expectation'' of the distribution (and also its median and mode). The parameter ''σ'' is its standard deviation; its variance is therefore σ'<sup> 2</sup>. A random variable with a Gaussian distribution is said to be '''normally distributed''' and is called a '''normal deviate'''. | The parameter ''μ'' in this formula is the ''mean'' or ''expectation'' of the distribution (and also its median and mode). The parameter ''σ'' is its standard deviation; its variance is therefore σ'<sup> 2</sup>. A random variable with a Gaussian distribution is said to be '''normally distributed''' and is called a '''normal deviate'''. | ||
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[[File:Cumulative Density Function.png]] | [[File:Cumulative Density Function.png]] | ||
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Revision as of 15:15, 3 August 2013
The normal distribution is
f(x) = (1⁄σ √2π ) e-((x-µ)2 ⁄ 2σ2)
The parameter μ in this formula is the mean or expectation of the distribution (and also its median and mode). The parameter σ is its standard deviation; its variance is therefore σ' 2. A random variable with a Gaussian distribution is said to be normally distributed and is called a normal deviate.
