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exponential random variable
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(Definition)
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$X$ is a exponential random variable with parameter $\lambda>0$ if its probability density function is given for $x>0$ by
To denote this, one usually writes $X\sim Exp(\lambda)$ .
For an exponential random variable $X$ :
- $X$ is commonly used to model lifetimes and duration between Poisson events.
- The expected value of $X$ is given by $E[X] = \frac{1}{\lambda}$
- The variance of $X$ is given by $Var[X] = \frac{1}{\lambda^2}$
- The moments of $X$ are given by $M_X(t) = \frac{\lambda}{\lambda - t}$
- It is interesting to note that $X$ is a gamma random variable with an $\alpha$ parameter of 1.
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"exponential random variable" is owned by mathcam. [ full author list (3) | owner history (2) ]
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| Other names: |
exponential distribution |
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Cross-references: gamma random variable, moments, variance, expected value, events, probability density function, parameter
There are 11 references to this entry.
This is version 4 of exponential random variable, born on 2001-10-26, modified 2004-04-09.
Object id is 528, canonical name is ExponentialRandomVariable.
Accessed 21509 times total.
Classification:
| AMS MSC: | 62E15 (Statistics :: Distribution theory :: Exact distribution theory) |
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Pending Errata and Addenda
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