For a Poisson random variable whose PMF is given by
![](https://test.transtutors.com/qimg/7944a2b9-9df4-4526-b54f-3b20c038f7d2.png)
k = 0,1,2...... , 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.