Problem 4. Smith has three records A,B,C which he keeps in a stack. (These are like mp3 files, bu...
Problem 4. Smith has three records A,B,C which he keeps in a stack. (These are like mp3 files, but come in the shape of a physical flat disc!) After he plays a record, he puts it at the top of the stack. His favourite is A, which he selects to listen with prob- ability 2/3. He selects B with probability 1/6, and he selects C also with probability 1/6. This defines a Markov chain, with the state of the system given by the differ- ent possible orders for the records. In your solution, order your states in the order ABC,ACB,BAC,BCA,CAB,CBA a) Write down the transition matrix for the Markov chain (b) Determine the stationary distribution of the Markov chain (c) Suppose the records are now in order BCA. How many steps will it take, on average, until the books are again in the same order?
Problem 4. Smith has three records A,B,C which he keeps in a stack. (These are like mp3 files, but come in the shape of a physical flat disc!) After he plays a record, he puts it at the top of the stack. His favourite is A, which he selects to listen with prob- ability 2/3. He selects B with probability 1/6, and he selects C also with probability 1/6. This defines a Markov chain, with the state of the system given by the differ- ent possible orders for the records. In your solution, order your states in the order ABC,ACB,BAC,BCA,CAB,CBA a) Write down the transition matrix for the Markov chain (b) Determine the stationary distribution of the Markov chain (c) Suppose the records are now in order BCA. How many steps will it take, on average, until the books are again in the same order?