Editing Mixture distribution (section)

===A normal and a Cauchy distribution===
The following example is adapted from Hampel,<ref>{{citation| last= Hampel | first= Frank | title= Is statistics too difficult? | journal= Canadian Journal of Statistics | year= 1998 | volume= 26 | pages= 497–513 | doi= 10.2307/3315772| hdl= 20.500.11850/145503 | hdl-access= free }}</ref> who credits [[John Tukey]].

Consider the mixture distribution defined by 
{{block indent | em = 1.6 | text = {{math|1=''F''(''x'') &nbsp; = &nbsp; (1 − 10<sup>−10</sup>) ([[Normal distribution|standard normal]]) + 10<sup>−10</sup> ([[Cauchy distribution|standard Cauchy]])}}.}}
The mean of [[i.i.d.]] observations from {{math|''F''(''x'')}} behaves "normally" except for exorbitantly large samples, although the mean of {{math|''F''(''x'')}} does not even exist.