Talk:Stieltjes moment problem

Latest comment: 3 years ago by Rumping in topic Positive Semi-Definiteness


Positive Semi-Definiteness

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Shouldn't the condition

 

(and possibly also  ) be relaxed to

 

(and possibly  )? At least

 

would imply that the Variance of a random variable is always strictly larger than zero, which for instance is not the case for the degenerate Dirac-distribution. — Preceding unsigned comment added by Imperialfists (talkcontribs) 19:57, 20 February 2016 (UTC)Reply

This is a slight issue with the finite support statement, and you have identified an   counterexample if   so   but  . Another counterexample happens with   and a Bernoulli random variable if   and   in which case   and so   but  , and I would expect this kind of counterexample to continue for all n whenever any of the n values in the support is 0 with positive probability. Rumping (talk) 01:55, 28 January 2021 (UTC)Reply