$E[X^4]$ for binomial random variable For a binomial random variable $X$ with parameters $n,p$, the expectations $E[X]$ and $E[X^2]$ are given be $np$ and $n(n-1)p^2+np$, respectively.
What about $E[X^4]$? Is there a table where I can look it up? Calculating it using the definition of expectation looks like a lot of work. Or is there a good way to calculate it?

Well, you can create a table if you know the moment generating function of $X$ i.e. $$M_X(t)=E[e^{tX}]$$ 
because $\frac{d^n}{dt^n}M_X(t)|_{t=0}=E[X^n].$ 
Hint: Show that $M_X(t)=(e^tp+(1-p))^n$ for binomial $X$ with parameters $n,p.$
