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Probability generating function ( $G_{X} (s) = E [s^{X}]$ )

For a nonnegative integer-valued random variable

X

, its probability generating function is

G_{X} (s) = E [s^{X}] = \sum_{n \geq 0} P (X = n) s^{n} .

The generating function of a sum of independent random variables is the product of their generating functions.

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