In a small remote neighbourhood consisting of Jr = 5 individuals, one individual is infected with a virus at time I]. Suppose that each pair of individuals in this neighbourhood meets at times of a Poisson process of rate 1 [independent of other meetings]. Meetings between an infected individual and an uninfected individual result in the uninfected individual being infected with probability p E {DJ}. Infected individuals remain infected for an Exponential amount of time with mean F: independent of everything else. Noone interacts with anyone from outside the town. Let N; denote the number of infected individuals at time t [so Nu = 1]. For the GTMC (Mites: {a} Draw the transition diagram. {b} Find the generator matrix. {c} Find all stationary distributions. {d} Find the probability that at some time everyone in the neighbourhood is {simultaneously} infected if p = a = 1. {e} Find the expected time until noone in the neighbourhood is infected by the virus when a=p=L