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Cauchy random variable
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(Definition)
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$X$ is a Cauchy random variable with parameters $\theta\in\R$ and $\beta>0\in\R$ , commonly denoted $X\sim Cauchy(\theta,\beta)$ if
Cauchy random variables are used primarily for theoretical purposes, the key point being that the values $E[X]$ and $Var[X]$ are undefined for Cauchy random variables.
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"Cauchy random variable" is owned by mathcam. [ full author list (2) | owner history (1) ]
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| Other names: |
Cauchy distribution |
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Cross-references: point, parameters
There are 5 references to this entry.
This is version 6 of Cauchy random variable, born on 2001-10-26, modified 2007-06-24.
Object id is 531, canonical name is CauchyRandomVariable.
Accessed 10717 times total.
Classification:
| AMS MSC: | 60A10 (Probability theory and stochastic processes :: Foundations of probability theory :: Probabilistic measure theory) |
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Pending Errata and Addenda
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![$\displaystyle f_X(x)=\frac{1}{\pi\beta[1+(\frac{x-\theta}{\beta})^2]}.$](http://images.planetmath.org:8080/cache/objects/531/js/img1.png "$\displaystyle f_X(x)=\frac{1}{\pi\beta[1+(\frac{x-\theta}{\beta})^2]}.$")