Difference between revisions of "Normal Command"
From GeoGebra Manual
m (better formula rendering) |
m |
||
Line 1: | Line 1: | ||
− | <noinclude>{{Manual Page|version= | + | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|probability}} |
− | {{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]]. | ||
Line 15: | Line 13: | ||
;Normal[ <Mean>, <Standard Deviation>, <Variable Value> ] | ;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''. | :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{ | + | :{{example| 1=<div><code><nowiki>Normal[2, 0.5, 1]</nowiki></code> yields <math>\frac{erf(-\sqrt{2})+1}{2}</math>.</div>}} |
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).
CAS Syntax
- 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}.