What's the meaning of ratio of second moment over third moment

Question

The random variable $X \sim D$, what's the meaning of this term? $$E[X^2]/E[X^3]$$ *$E[X^3]$ is the third raw moment.

Answer 1

Skewness is $$S = \frac{E[X^3]-3\mu\sigma^2-\mu^3}{\sigma^3}$$. In the special case of $\mu = 0$, this simplifies to $E[X^3]/\sigma^3$ Meanwhile variance is $$\sigma^2 = E[X^2]-E[X]^2$$ so if $\mu=0$ that simplifies to $E[X^2]$. So in this case, your expression $$\frac{E[X^2]}{E[X^3]}= \frac{\sigma^2}{S\sigma^3} = \frac{1}{S\sigma}$$

I don't see what the significance of the expression is, but that is a simplified case.