People arrive at a restaurant by families. The number of families X that arrive over the period of 1 hour is found to be a Poisson random variable with rate λ. If the number of people in each arriving family is a random variable N whose PMF has the z-transform that is given by
Determine the following:
a. GM(z), the z-transform of the PMF of M, which is the total number of people arriving at the restaurant in an arbitrary hour
b. E[Y], where Y is the total number of people that arrive at the restaurant over a three-hour period