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$W$ is a random variable with $E[(W−μ)^3]=10$ and $E(W^3)=4$. Is it possible that $μ=2$?

Am I supposed to find the skewness?

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    You have not said whether $E[W]=\mu$ (though given Robert Israel's answer it may not matter). If it is then you can find $E(W^2)=-36$.2012-04-09

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If $\mu > 0$, $(x-\mu)^3 < x^3$ for all real numbers $x$ (because $x^3$ is an increasing function of $x$). What would that say about the relationship between $E[(W-\mu)^3]$ and $E[W^3]$?