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 $X$ $s$ are:


 * $\dfrac {\d^k} {\d s^k} \map {\Pi_X} s = \begin{cases}

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