Difference between revisions of "Exponential Command"
From GeoGebra Manual
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{{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.