5. (Problem 3.1.1 in Pinksy and Karlin) A simplied model for the spread of a disease goes this way: The total pepulation size is N = 4, of which some are diseased and the remainder are healthy. During any single period of time, two people are selected are random from the population and assumed to interact. The selection is such that an encounter between any pair of individuals in the population is just as likely as between any other pair. If one of these persons is diseased and the other not, with probability a = 0.1 the disease is transmitted to the healthy person. Otherwise, no disease transmission takes place. Let Xn denote the number of diseased persons in the population at the end of the nth period. Specify the transition probability matrix, justify your