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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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Expand the product $(W-\mu)^{3}$ and use the linearity of expectation. Substitute in the given values, making sure to remember that the assumed value $\mu=2=E[W]$, and see if what results will admit a sensible solution. – Mr. F Apr 9 '12 at 22:16
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 $E(W^2)=-36$. – Henry Apr 9 '12 at 22:53
up vote 5 down vote accepted

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 $E[W^3]$?

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