Difference between revisions of "Exponential Command"

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<noinclude>{{Manual Page|version=4.0}}</noinclude>
 
<noinclude>{{Manual Page|version=4.0}}</noinclude>
 
{{command|probability}}
 
{{command|probability}}
;Exponential[ <Mean λ>, x ]
+
;Exponential[ <Rate parameter λ>, x ]
:Creates probability density function (pdf) of [[w:Exponential distribution|exponential distribution]] with mean λ.
+
:Creates probability density function (pdf) of [[w:Exponential distribution|exponential distribution]] with rate parameter λ.
;Exponential[ <Mean λ>, x, <Boolean Cumulative> ]
+
;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[ <Mean 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 mean λ.
+
;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[ <Mean λ>, <Variable Value v>]
+
;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 mean λ.
+
: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.
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