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[2, 1]</nowiki></code> gives | + | :{{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 11:05, 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.