Suppose a dinner clubs eats out once a week, and the members have a choice of Chinese, Italian, or American cuisine. They never eat the same cuisine two weeks in a row. If they have Chinese one week they are twice as likely to have American as Italian the following week. If they have Italian one week, they are equally likely to have Chinese as American the next week. If they have American one week, they are twice as likely to have Chinese as Italian the next week. 1. Make the transition matrix P for this Markov Chain (MC). 2. If they have American the first week, what is the probablility they have Chinese the fifth week? 3. Estimate the long term fraction of the time they have each cuisine.