Difference between revisions of "Exponential Command"
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:{{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== | ||
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;Exponential[ <Rate parameter 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 rate parameter ''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> 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 10:33, 11 January 2013
- 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
- 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]yields \frac{e^{2} - 1}{e^{2} } , which is approximately 0.86.
