For completeness, there are also distributions for which the mean is not well defined. A classic example is the Cauchy distribution ([this answer][1] has a nice explanation of why). Another important example is the [Pareto distribution][2] with exponent less than 2.


  [1]: https://stats.stackexchange.com/questions/36027/why-does-the-cauchy-distribution-have-no-mean
  [2]: https://en.wikipedia.org/wiki/Power_law#Lack_of_well-defined_average_value