# 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 expansion of HX( z) about the point z = 1 ,

(c) A general expression for the k th factorial moment.

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.

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