Is there a way to provide a Select All / Check All checkbox for a field that displays multiple checkboxes in Drupal 7?

Notice that $X \stackrel{d}{=} 2 U - n$, where $U$ follows binomial distribution $Bi(n, \frac{1}{2})$. Moment generating function of the symmetric binomial distribution is $g(t) = \mathbb{E}\left( \mathbb{e}^{t U} \right) = \left( \frac{1}{2} + \frac{1}{2} \mathrm{e}^t \right)^n$. Therefore

$$ \mathbb{E}\left( \mathbb{e}^{t X} \right) = \mathrm{e}^{-t n} g(2t) = \cosh^n(t) $$

The fourth moment can be extracted from series expansion: $$ \cosh^n(t) = 1 + n \frac{t^2}{2!} + n(3n-2) \frac{t^4}{4!} + o(t^4) $$