- #1
Neothilic
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- TL;DR Summary
- Proving how the Cauchy distribution has no moments for all n.
How can I prove the Cauchy distribution has no moments?
##E(X^n)=\int_{-\infty}^\infty\frac{x^n}{\pi(1+x^2)}\ dx.##
I can prove myself, letting ##n=1## or ##n=2## that it does not have any moment. However, how would I prove for ALL ##n##, that the Cauchy distribution has no moments?
##E(X^n)=\int_{-\infty}^\infty\frac{x^n}{\pi(1+x^2)}\ dx.##
I can prove myself, letting ##n=1## or ##n=2## that it does not have any moment. However, how would I prove for ALL ##n##, that the Cauchy distribution has no moments?