Difference between revisions of "Normal Command"

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<noinclude>{{Manual Page|version=4.0}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude>
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|probability}}
{{command|probability}}
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;Normal( <Mean>, <Standard Deviation>, x )
<!-- DO NOT TRANSLATE, STILL MESSY -->
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:Creates cumulative density function (cdf) of [[w:Normal distribution|normal distribution]].
;Normal[Mean μ, Standard Deviation σ, x ]
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:Creates probability density function (pdf) of [[w:Normal distribution|normal distribution]].
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;Normal( <Mean>, <Standard Deviation>, x, <Boolean Cumulative> )
;Normal[Mean μ, Standard Deviation σ, x, Boolean Cumulative]
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:If ''Cumulative'' is true, creates cumulative distribution function of normal distribution with mean μ and standard deviation σ, otherwise creates pdf of normal distribution.
:If ''Cumulative'' is true, creates cumulative density function of normal distribution, otherwise creates pdf of normal distribution.
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; Normal[Mean μ, Standard Deviation σ, Variable Value x]: Calculates the function ''Φ((x – μ) / σ)'' where ''Φ'' is the cumulative density function for ''N(0,1)''.
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;Normal( <Mean μ>, <Standard Deviation σ>, <Variable Value v> )
:{{Note| Returns the probability for a given ''x''-coordinate's value (or area under the normal distribution curve to the left of the given ''x''-coordinate).}}
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:Calculates the function <math>\Phi \left(\frac{x- \mu}{\sigma} \right) </math> at ''v'' where ''Φ'' is the cumulative distribution function for ''N(0,1)'' with mean ''μ'' and standard deviation ''σ''.
==CAS Syntaxes==
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:{{note| Returns the probability for a given ''x''-coordinate's value (or area under the normal distribution curve to the left of the given ''x''-coordinate).}}
In [[CAS View]] only following syntax is supported:
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;Normal[Mean μ, Standard Deviation σ, Variable Value x]
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:{{example| 1=<code><nowiki>Normal(2, 0.5, 1)</nowiki></code> yields ''0.02'' in the [[File:Menu view algebra.svg|links=|16px]] [[Algebra View]] and <math>\frac{erf(-\sqrt{2})+1}{2}</math> in the [[File:Menu view cas.svg|links=|16px]] [[CAS View]].}}
: Calculates the function ''Φ((x – μ) / σ)'' where ''Φ'' is the cumulative density function for ''N(0,1)''.
 

Latest revision as of 11:13, 30 July 2019


Normal( <Mean>, <Standard Deviation>, x )
Creates cumulative density function (cdf) of normal distribution.
Normal( <Mean>, <Standard Deviation>, x, <Boolean Cumulative> )
If Cumulative is true, creates cumulative distribution function of normal distribution with mean μ and standard deviation σ, otherwise creates pdf of normal distribution.
Normal( <Mean μ>, <Standard Deviation σ>, <Variable Value v> )
Calculates the function \Phi \left(\frac{x- \mu}{\sigma} \right) at v where Φ is the cumulative distribution function for N(0,1) with mean μ and standard deviation σ.
Note: Returns the probability for a given x-coordinate's value (or area under the normal distribution curve to the left of the given x-coordinate).
Example: Normal(2, 0.5, 1) yields 0.02 in the links= Algebra View and \frac{erf(-\sqrt{2})+1}{2} in the links= CAS View.
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