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I would like to know if it is possible to find an unbiased estimator for the product of the variance of a random variable and its expected value.

And in general, an unbiased estimator of the product of a central moment of a random variable and its expected value.

I'm aware of Polyaches (unbiased estimators of products of central moments) and PolyRaws (unbiased estimators of products of raw moments). But what about the product of central and raw moments?

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