$W$ 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?
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 $E[W^3]$?