# Difference between revisions of "Exponential Command"

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;Exponential( <Lambda>, <Variable Value> ) | ;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= | + | :{{example| 1=<code><nowiki>Exponential(2, 1)</nowiki></code> yields ''<math>1 - \frac{1}{e^{2} } </math>'', which is approximately ''0.86''.}} |

## Revision as of 11:11, 11 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*.