Question: For a Poisson random variable whose PMF is given by Find the following: (a) The probability- generating function, HX( z) , (b) The Taylor series

For a Poisson random variable whose PMF is given by

Find the following:
(a) The probability- generating function, HX( z) ,
(b) The Taylor series expansion of HX( z) about the point z = 1 ,
(c) A general expression for the k th factorial moment.

P(k) k! k = 0, 1, 2, .., %3D

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