Question: Suppose HX( z) is the probability- generating function of some random variable X with PMF PX( k) . In terms of PX( k) , find

Suppose HX( z) is the probability- generating function of some random variable X with PMF PX( k) . In terms of PX( k) , find the PMF of the random variable Y if its probability- generating function is given as in each of the following cases.
(a) HY (z) = HX (z / 2)
(b) HY (z) = HX 2 = ( z) .
(c) HY (z) = zmHX( z) .
(d) HY (z) = HX( z– 1).

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