Difference between revisions of "Normal Command"

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(removed extra CAS syntax)
m (Text replace - ";(.*)\[(.*)\]" to ";$1($2)")
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|probability}}
 
<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|probability}}
;Normal[ <Mean>, <Standard Deviation>, x ]
+
;Normal( <Mean>, <Standard Deviation>, 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>, <Standard Deviation>, x, <Boolean Cumulative> ]
+
;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.
 
: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> ]
+
;Normal( <Mean μ>, <Standard Deviation σ>, <Variable Value v> )
 
: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''.
 
: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''.
 
:{{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).}}
 
:{{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| 1=<div><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]].</div>}}
 
:{{example| 1=<div><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]].</div>}}

Revision as of 17:16, 7 October 2017


Normal( <Mean>, <Standard Deviation>, x )
Creates probability density function (pdf) 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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