Noun
Cauchy distribution (plural Cauchy distributions)
(statistics) A symmetric continuous probability distribution with fat tails, with probability density function that is
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{\displaystyle {\begin{aligned}f(x;x_{0},\gamma )&={\frac {1}{\pi \gamma \left[1+\left({\frac {x-x_{0}}{\gamma }}\right)^{2}\right]}}&={1 \over \pi }\left[{\gamma \over (x-x_{0})^{2}+\gamma ^{2}}\right]\end{aligned}}}
For example, the standard deviation of a random variable that follows a Cauchy distribution is undefined because its expected value μ is undefined. Source: Internet
Not every probability distribution has a defined mean; see the Cauchy distribution for an example. Source: Internet