Derivatives of PGF of Bernoulli Distribution

Theorem
Let $X$ be a discrete random variable with the Bernoulli distribution with parameter $p$.

Then the derivatives of the PGF of $X$ w.r.t. $s$ are:


 * $\dfrac {\mathrm d^k} {\mathrm d s^k} \Pi_X \left({s}\right) = \begin{cases}

p & : k = 1 \\ 0 & : k > 1 \end{cases}$