You work for the CDC and have been called in to consult about the appearance in Connecticut of a single zombie. It is known from studies of past zombie epidemics, that for this strain of the zombie virus, the probability that a zombie infects one human before the zombie is killed is P(1) = a and the probability that a zombie infects two humans before the zombie is killed is P(2) a, and that, for this strain, no-more than two humans can be infected per zombie. Once infected a human quickly turns into a zombie. (a) What is the probability that a zombie infects zero humans? (b) Calculate the mean number of people infected by each zombie, (k)? For what range of values of a is (k) > 1? (c) If Q is the probability that the infection from a zombie eventually dies out, we can determine Q by solving: Q= (1-a-a)+aQ+a Q2. Explain each term in EQ. 5.73. (d) Find Q and the range of values of a for which the US population as a whole is safe from the zombie apocalypse. (e) Plot your solution for Q from (d) for