Difference between revisions of "Exponential Command"
From GeoGebra Manual
Noel Lambert (talk | contribs) |
|||
| Line 1: | Line 1: | ||
<noinclude>{{Manual Page|version=4.0}}</noinclude> | <noinclude>{{Manual Page|version=4.0}}</noinclude> | ||
{{command|probability}} | {{command|probability}} | ||
| − | ;Exponential[ < | + | ;Exponential[ <Rate parameter λ>, x ] |
| − | :Creates probability density function (pdf) of [[w:Exponential distribution|exponential distribution]] with | + | :Creates probability density function (pdf) of [[w:Exponential distribution|exponential distribution]] with rate parameter λ. |
| − | ;Exponential[ < | + | ;Exponential[ <Rate parameter λ>, x, <Boolean Cumulative> ] |
:If ''Cumulative'' is true, creates cumulative distribution function (cdf) of exponential distribution, otherwise creates pdf of Exponential distribution. | :If ''Cumulative'' is true, creates cumulative distribution function (cdf) of exponential distribution, otherwise creates pdf of Exponential distribution. | ||
| − | ;Exponential[ < | + | ;Exponential[ <Rate parameter λ>, <Variable Value v> ]: Calculates the value of cumulative distribution function of Exponential distribution at ''v'', i.e. the probability ''P(X≤v)'' where ''X'' is a random variable with Exponential distribution with rate parameter λ. |
:{{Note| Returns the probability for a given ''x''-coordinate's value (or area under the Exponential 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 Exponential distribution curve to the left of the given ''x''-coordinate).}} | ||
==CAS Syntax== | ==CAS Syntax== | ||
In [[CAS View]] only following syntax is supported: | In [[CAS View]] only following syntax is supported: | ||
| − | ;Exponential[ < | + | ;Exponential[ <Rate parameter λ>, <Variable Value v>] |
| − | :Calculates the value of cumulative distribution function of exponential distribution at ''v'', i.e. the probability ''P(X≤v)'' where ''X'' is a random variable with Exponential distribution with | + | :Calculates the value of cumulative distribution function of exponential distribution at ''v'', i.e. the probability ''P(X≤v)'' where ''X'' is a random variable with Exponential distribution with rate parameter λ. |
:{{example|1=<div><code><nowiki>Exponential[2, 1]</nowiki></code> gives <math>\frac{e^{2}-1}{e^{2} } </math>, which is approximately ''0.86''.</div>}} | :{{example|1=<div><code><nowiki>Exponential[2, 1]</nowiki></code> gives <math>\frac{e^{2}-1}{e^{2} } </math>, which is approximately ''0.86''.</div>}} | ||
Revision as of 14:44, 8 August 2011
- Exponential[ <Rate parameter λ>, x ]
- Creates probability density function (pdf) of exponential distribution with rate parameter λ.
- Exponential[ <Rate parameter λ>, x, <Boolean Cumulative> ]
- If Cumulative is true, creates cumulative distribution function (cdf) of exponential distribution, otherwise creates pdf of Exponential distribution.
- Exponential[ <Rate parameter λ>, <Variable Value v> ]
- Calculates the value of cumulative distribution function of Exponential distribution at v, i.e. the probability P(X≤v) where X is a random variable with Exponential distribution with rate parameter λ.
- Note: Returns the probability for a given x-coordinate's value (or area under the Exponential distribution curve to the left of the given x-coordinate).
CAS Syntax
In CAS View only following syntax is supported:
- Exponential[ <Rate parameter λ>, <Variable Value v>]
- Calculates the value of cumulative distribution function of exponential distribution at v, i.e. the probability P(X≤v) where X is a random variable with Exponential distribution with rate parameter λ.
- Example:
Exponential[2, 1]gives \frac{e^{2}-1}{e^{2} } , which is approximately 0.86.
