Difference between revisions of "Normal Command"

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

Algebra View and \frac{erf(-\sqrt{2})+1}{2} in the

CAS View.

@@ Line 1: / Line 1: @@
-<noinclude>{{Manual Page|version=4.0}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude>
+<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|probability}}
-{{command|probability}}
+;Normal( <Mean>, <Standard Deviation>, x )
-;Normal[Mean μ, Standard Deviation σ, x ]
+:Creates cumulative density function (cdf) 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>, <Standard Deviation>, x, <Boolean Cumulative> )
-:If ''Cumulative'' is true, creates cumulative density function of normal distribution, 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 x]: Calculates the function ''Φ((x – μ) / σ)'' where ''Φ'' is the cumulative density 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).}}
+;Normal( <Mean μ>, <Standard Deviation σ>, <Variable Value v> )
-==CAS Syntaxes==
+: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''.
-In [[CAS View]] only following syntax is supported:
+:{{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 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)''.
+:{{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]].}}

Difference between revisions of "Normal Command"

Latest revision as of 11:13, 30 July 2019

Normal

Command Categories (All commands)