Cauchy Distribution has no Finite Moments

Theorem

The Cauchy distribution has no finite moments.

That is, for example, it has no defined:

expectation
variance
moment generating function

and so on.


Proof


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Sources

  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Cauchy distribution
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Cauchy distribution
  • 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Cauchy distribution
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