Random Pub Crawl: Your town has 5 pubs close to your home, say A, B, C, D, E. 1/4 1/2 B 1/2 Home 1/2 1/4 1/4 1/4 1/4 1/4 1/3 1/3 1/2 1/1 D E 1/3 1/2 Write a program to simulate from the random pub crawl. (From the "home" state allow probability 1/2 of going back to the Royal Oak). Starting from the Home state, run your program 1000 times, each time simulating a Markov chain of length 100. Each simulation should be a random sequence of values (81, 82, 83 ...,S100where each s; is a pub. Collect statistics of the number of times each state is visited at each time step t = 1,...,100. How do the statistics defer if you started at D? Does the distribution over states visited at step t converge for large t? Approximately how long does it take for the chain to "forget"" whether it started at Home or at D? Random Pub Crawl: Your town has 5 pubs close to your home, say A, B, C, D, E. 1/4 1/2 B 1/2 Home 1/2 1/4 1/4 1/4 1/4 1/4 1/3 1/3 1/2 1/1 D E 1/3 1/2 Write a program to simulate from the random pub crawl. (From the "home" state allow probability 1/2 of going back to the Royal Oak). Starting from the Home state, run your program 1000 times, each time simulating a Markov chain of length 100. Each simulation should be a random sequence of values (81, 82, 83 ...,S100where each s; is a pub. Collect statistics of the number of times each state is visited at each time step t = 1,...,100. How do the statistics defer if you started at D? Does the distribution over states visited at step t converge for large t? Approximately how long does it take for the chain to "forget"" whether it started at Home or at D