Question: 5.1.3 The generating function of a probability mass function pk D PrfX D kg, for k D 0;1; : : : ; is defined by

5.1.3 The generating function of a probability mass function pk D PrfX D kg, for k D 0;1; : : : ; is defined by

8x(s) =E[s]=Pks for |s|

Show that the generating function for a Poisson random variable X with mean is given by

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8x(s) =E[s]=Pks for |s|

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