Difference between revisions of "Exponential Command"
From GeoGebra Manual
m (Text replace - "<div class="box info"> 48px|left This page is part of the official manual for print and pdf. For structural reasons normal users can't edit this page. If you found any errors on this page please contact ) |
|||
| Line 1: | Line 1: | ||
<noinclude>{{Manual Page|version=4.2}}</noinclude> | <noinclude>{{Manual Page|version=4.2}}</noinclude> | ||
{{command|cas=true|probability}} | {{command|cas=true|probability}} | ||
| − | ;Exponential[ < | + | ;Exponential[ <Lambda>, 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 parameter ''lambda''. |
| − | ;Exponential[ < | + | ;Exponential[ <Lambda>, 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[ <Lambda>, <Variable Value> ] |
| − | :Calculates the value of cumulative distribution function of Exponential distribution at ''v'', i.e. the probability ''P( | + | :Calculates the value of cumulative distribution function of Exponential distribution at variable value ''v'', i.e. the probability ''P(X ≤ v)'' where ''X'' is a random variable with Exponential distribution with parameter ''lambda''. |
:{{note| 1=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| 1=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== | ||
| − | ;Exponential[ < | + | ;Exponential[ <Lambda>, <Variable Value> ] |
| − | :Calculates the value of cumulative distribution function of exponential distribution at ''v'', i.e. the probability ''P( | + | :Calculates the value of cumulative distribution function of exponential distribution at variable value ''v'', i.e. the probability ''P(X ≤ v)'' where ''X'' is a random variable with Exponential distribution with parameter ''lambda''. |
:{{example| 1=<div><code><nowiki>Exponential[2, 1]</nowiki></code> yields ''<math>\frac{e^{2} - 1}{e^{2} } </math>'', which is approximately ''0.86''.</div>}} | :{{example| 1=<div><code><nowiki>Exponential[2, 1]</nowiki></code> yields ''<math>\frac{e^{2} - 1}{e^{2} } </math>'', which is approximately ''0.86''.</div>}} | ||
Revision as of 14:47, 21 May 2013
- Exponential[ <Lambda>, x ]
- Creates probability density function (pdf) of exponential distribution with parameter lambda.
- Exponential[ <Lambda>, x, <Boolean Cumulative> ]
- If Cumulative is true, creates cumulative distribution function (cdf) of exponential distribution, otherwise creates pdf of Exponential distribution.
- Exponential[ <Lambda>, <Variable Value> ]
- Calculates the value of cumulative distribution function of Exponential distribution at variable value v, i.e. the probability P(X ≤ v) where X is a random variable with Exponential distribution with parameter lambda.
- 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
- Exponential[ <Lambda>, <Variable Value> ]
- Calculates the value of cumulative distribution function of exponential distribution at variable value v, i.e. the probability P(X ≤ v) where X is a random variable with Exponential distribution with parameter lambda.
- Example:
Exponential[2, 1]yields \frac{e^{2} - 1}{e^{2} } , which is approximately 0.86.
