Difference between revisions of "Normal Command"

Revision as of 13:44, 6 August 2015

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).

Normal[ <Mean>, <Standard Deviation>, <Variable Value> ]: Calculates the function \Phi \left(\frac{x- \mu}{\sigma} \right) where Φ is the cumulative distribution function for N(0,1) with mean μ and standard deviation σ.; Example:
Normal[2, 0.5, 1] yields \frac{erf(-\sqrt{2})+1}{2}.

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-<noinclude>{{Manual Page|version=4.2}}</noinclude>
+<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|probability}}
-{{command|cas=true|probability}}
 ;Normal[ <Mean>, <Standard Deviation>, x ]
 :Creates probability density function (pdf) of [[w:Normal distribution|normal distribution]].
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 ;Normal[ <Mean>, <Standard Deviation>, <Variable Value> ]
 :Calculates the function  <math>\Phi \left(\frac{x- \mu}{\sigma} \right) </math> where ''Φ'' is the cumulative distribution function for ''N(0,1)'' with mean ''μ'' and standard deviation ''σ''.
-:{{example| 1=<div><code><nowiki>Normal[2, 0.5, 1]</nowiki></code> yields <math>\frac{-erf(2/\sqrt{2})+1}{2}</math>.</div>}}
+:{{example| 1=<div><code><nowiki>Normal[2, 0.5, 1]</nowiki></code> yields <math>\frac{erf(-\sqrt{2})+1}{2}</math>.</div>}}