Contagion Under certain conditions, the probability that a person will get a particular contagious disease and die from it is 0.05, and the probability of getting the disease and surviving is 0.15. The probability that a survivor will infect another person who dies from it is also 0.05, that a survivor will infect another person who survives it is 0.15, and so on. A transition matrix using the following stales is given below. A person in state 1 is one who gets the disease and dies, a person in stale 2 gets the disease and survives, and a person in slate 3 does not get the disease. Consider a chain of people, each of whom interacts with the previous person and may Catch the disease from that individual, and then may infect the next person.
(a) Verify that the transition matrix is as follows:
(b) Find F and FR.
(c) Find the probability that the disease eventually disappears.
(d) Given a person who has the disease and survives, find the expected number of people in the chain who will get the disease until a person who does not get the disease is reached.
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Finite Mathematics (11th Edition)
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning