I am trying to find the value of a skewed distribution but can't make sense of what to plug in to evaluate the answer.
This is the given:
$ \text{Let X be Binomial(n, p). } \text{Using that, evaluate:} $ $ \beta = \frac{E[(X-\mu)^3]}{\sigma^3} $
Now, I expanded the numerator and got this: (wikipedia)
$ \beta = \frac{E[X^3] - 3\mu\sigma^2 - \mu^3}{\sigma^3} $
and I know that $\mu=np$ and $\sigma=\sqrt{3np(1-p)}$ and this is what it simplifies to from what I did
$ \beta = \frac{E[X^3] - 3np(3np(1-p)) - (np)^3}{(\sqrt{3np(1-p)})^3} $
The Problem
The issue is that I can't make sense of $E[X^3]$. I don't know how to evaluate that in order to get a numerical value of $\beta$ for arbitrary n and p values. The binomial distribution should take arguments x, n and p right? What is x here?
Would $E[X^3]$ be just $(np)^3$?
Thanks