Difference between revisions of "Exponential Command"

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;Exponential[ <Mean λ>, <Variable Value v>]
 
;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.
 
: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.
:{{example|1=<div><code><nowiki>Exponential[4, 3]</nowiki></code> gives ''<math>\frac{d<sup>12</sup>-1}{e12}</math>'', the sum of all positive divisors of ''15'', including ''15''.</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 11:09, 5 August 2011



Exponential[ <Mean λ>, x ]
Creates probability density function (pdf) of exponential distribution with mean λ.
Exponential[ <Mean λ>, x, <Boolean Cumulative> ]
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.
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[ <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.
Example:
Exponential[2, 1] gives \frac{e^{2}-1}{e^{2}}, which is approximately 0.86.
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