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 | + | ;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 | + | ;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 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 | + | ;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.
