What is $$\sup_X \frac{\mathbb E(X^3)\mathbb E(X)}{(\mathbb E(X^2))^2}$$ for X a non-negative random variable? I think the min is reached in Dirac masses, but for the max I don't find it.
2026-05-14 12:36:14.1778762174
Maximum of the ratio of some moments of a non-negative random variable
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