Difference between revisions of "Normal Command"

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<noinclude>{{Manual Page|version=4.0}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude>
 
<noinclude>{{Manual Page|version=4.0}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude>
 
{{command|probability}}
 
{{command|probability}}
;Normal[Mean μ, Standard Deviation σ, x ]
+
;Normal[ <Mean μ>, <Standard Deviation σ>, <x> ]
 
:Creates probability density function (pdf) of [[w:Normal distribution|normal distribution]].
 
:Creates probability density function (pdf) of [[w:Normal distribution|normal distribution]].
;Normal[Mean μ, Standard Deviation σ, x, Boolean Cumulative]
+
;Normal[ <Mean μ>, <Standard Deviation σ>, <x>, <Boolean Cumulative> ]
 
:If ''Cumulative'' is true, creates cumulative distribution function of normal distribution, otherwise creates pdf of normal distribution.
 
:If ''Cumulative'' is true, creates cumulative distribution function of normal distribution, otherwise creates pdf of normal distribution.
;Normal[Mean μ, Standard Deviation σ, Variable Value v]: Calculates the function ''Φ((x – μ) / σ)'' at ''v'' where ''Φ'' is the cumulative distribution function for ''N(0,1)''.
+
;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).}}
+
:Calculates the function ''Φ((x – μ) / σ)'' at ''v'' where ''Φ'' is the cumulative distribution function for ''N(0,1)''.
 +
:{{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).}}
 
==CAS Syntaxes==
 
==CAS Syntaxes==
 
In [[CAS View]] only following syntax is supported:
 
In [[CAS View]] only following syntax is supported:
;Normal[Mean μ, Standard Deviation σ, Variable Value x]
+
;Normal[ <Mean μ>, <Standard Deviation σ>, <Variable Value x> ]
 
:Calculates the function ''Φ((x – μ) / σ)'' where ''Φ'' is the cumulative distribution function for ''N(0,1)''.
 
:Calculates the function ''Φ((x – μ) / σ)'' where ''Φ'' is the cumulative distribution function for ''N(0,1)''.
 
:{{example| 1=<div><code><nowiki>Normal[2, 0.5, 1]</nowiki></code> yields <math>0.5 erf(-\sqrt{2}) + 0.5</math>.</div>}}
 
:{{example| 1=<div><code><nowiki>Normal[2, 0.5, 1]</nowiki></code> yields <math>0.5 erf(-\sqrt{2}) + 0.5</math>.</div>}}

Revision as of 13:08, 22 August 2011


Normal[ <Mean μ>, <Standard Deviation σ>, <x> ]
Creates probability density function (pdf) of normal distribution.
Normal[ <Mean μ>, <Standard Deviation σ>, <x>, <Boolean Cumulative> ]
If Cumulative is true, creates cumulative distribution function of normal distribution, otherwise creates pdf of normal distribution.
Normal[ <Mean μ>, <Standard Deviation σ>, <Variable Value v> ]
Calculates the function Φ((x – μ) / σ) at v where Φ is the cumulative distribution function for N(0,1).
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).

CAS Syntaxes

In CAS View only following syntax is supported:

Normal[ <Mean μ>, <Standard Deviation σ>, <Variable Value x> ]
Calculates the function Φ((x – μ) / σ) where Φ is the cumulative distribution function for N(0,1).
Example:
Normal[2, 0.5, 1] yields 0.5 erf(-\sqrt{2}) + 0.5.
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