Difference between revisions of "Normal Command"

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;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>}}
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:{{example| 1=<div><code><nowiki>Normal[2, 0.5, 1]</nowiki></code> yields <math>\frac{\sqrt{2}&#125;{\sqrt{\pi }e²}</math>.</div>}}

Revision as of 19:10, 13 February 2012


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 \frac{\sqrt{2}}{\sqrt{\pi }e²}.
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