For a particular infectious disease, the number of distinct uninfected peo- ple, N, infected by a single infected person has a distribution with prob- 1- ability generating function P(2) = 1 12. A pandemic begins with a single infected person, and the numbers of people infected by different people are independent. (a) What is the probability that the pandemic ever dies out (i.e. that only a finite number of total infections happen)? (b) What is the "probability generating function" for the total number of people infected? [Technically, since there is non-zero probability that this number is infinite, it is not a probability generating function.]