\fPart (a) Why is column 1 all zeros except the top number? Part (b) Are any states absorbing or transient? Is the system ergodic? Part (c) A certain person has never interacted with the health system. What is the probability that he never interacts with it apart from his death? (Hint: look at the first row of the transition matrix) Part (d) Discuss the Markov assumptions in the context of this process. Are the Markov assumptions realistic? Give some reasons why the states are not a Markov chain; which of the Markov assumptions are likely to be broken? Part (e) Write some R code to simulate the above Markov chain. Use your R code to answer the following questions: . How many interactions with the health system can a person expect in their lifetime? . A person is in hospital. How many subsequent visits to hospital can we expect for this person? . A person is at the pharmacist. What is the distribution for the number of visits to a pharmacist without visiting the GP or hospital? . What is the probability that someone's last interaction with the health service was a hospital visit