Binomiale

$\displaystyle G(t\,\vert\,{\cal B}_{n,p})$	$\displaystyle =$	$\displaystyle \sum_{x=0}^ne^{t\, x}\, \binom{n}{x} \, p^x\, q^{n-x}$
	$\displaystyle =$	$\displaystyle \sum_{x=0}^n \binom{n}{x} \, \left(e^t\, p\right)^x \, q^{n-x}$
	$\displaystyle =$	$\displaystyle \left( e^t\, p+q\right)^n.$

E $\displaystyle (X)$	$\displaystyle =$	$\displaystyle \left. n\, p\, e^t\, \left(e^t\, p+q\right)^{n-1}\right\vert _{t=0} = n\, p$

E $\displaystyle (X^2)$	$\displaystyle =$	$\displaystyle \left[n\, (n-1)\, \left(p\, e^t\right)^2 \, \left(e^t\, p+q\right)^{n-2}\right.$
		$\displaystyle \left.\left. + n\, p\, e^t\, \left(e^t\, p+q\right)^{n-1}\right]\right\vert _{t=0}$
	$\displaystyle =$	$\displaystyle n\, (n-1)\, p^2+n\, p$
Var $\displaystyle (X)$	$\displaystyle =$	$\displaystyle n\, p\, q \,.$