Difference between revisions of "Exponential Command"

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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|probability}}
 
<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|probability}}
;Exponential[ <Lambda>, x ]
+
;Exponential( <Lambda>, x )
 
:Creates probability density function (pdf) of [[w:Exponential distribution|exponential distribution]] with parameter ''lambda''.
 
:Creates probability density function (pdf) of [[w:Exponential distribution|exponential distribution]] with parameter ''lambda''.
;Exponential[ <Lambda>, x, <Boolean Cumulative> ]
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;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[ <Lambda>, <Variable Value> ]
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;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''.
 
: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[ <Lambda>, <Variable Value> ]
+
;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''.
 
: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>1 - \frac{1}{e^{2} } </math>'', which is approximately  ''0.86''.</div>}}
 
:{{example| 1=<div><code><nowiki>Exponential[2, 1]</nowiki></code> yields ''<math>1 - \frac{1}{e^{2} } </math>'', which is approximately  ''0.86''.</div>}}

Revision as of 17:15, 7 October 2017


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 1 - \frac{1}{e^{2} } , which is approximately 0.86.
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