Derivatives of PGF of Negative Binomial Distribution/Second Form
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Theorem
Let $X$ be a discrete random variable with the negative binomial distribution (second form) with parameters $n$ and $p$.
Then the derivatives of the PGF of $X$ with respect to $s$ are:
- $\dfrac {\d^k} {\d s^k} \map {\Pi_X} s = ...$
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Proof
The Probability Generating Function of Negative Binomial Distribution (Second Form) is:
- $\map {\Pi_X} s = \paren {\dfrac {p s} {1 - q s} }^n$
We have that for a given negative binomial distribution , $n, p$ and $q$ are constant.
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