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Talk:Stieltjes moment problem

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Positive Semi-Definiteness

[edit]

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]