Difference between revisions of "Normal Command"
From GeoGebra Manual
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{{command|cas=true|probability}} | {{command|cas=true|probability}} | ||
| − | ;Normal[ <Mean | + | |
| + | ;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 | + | |
| − | :If ''Cumulative'' is true, creates cumulative distribution function of normal distribution, otherwise creates 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> ] | ;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)''. | + | :Calculates the function ''Φ((x – μ) / σ)'' 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).}} | ||
| + | |||
==CAS Syntax== | ==CAS Syntax== | ||
| − | ;Normal[ <Mean | + | ;Normal[ <Mean>, <Standard Deviation>, <Variable Value> ] |
| − | :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)'' with mean ''μ'' and standard deviation ''σ''. |
| − | :{{example| 1=<div><code><nowiki>Normal[2, 0.5, 1]</nowiki></code> yields <math>\frac{\sqrt{2} | + | :{{example| 1=<div><code><nowiki>Normal[2, 0.5, 1]</nowiki></code> yields <math>\frac{-erf(2/\sqrt{2})+1}{2}</math>.</div>}} |
Revision as of 09:19, 10 July 2013
- 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 Φ((x – μ) / σ) 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 Φ((x – μ) / σ) 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(2/\sqrt{2})+1}{2}.
