Find the transition matrix for the chain. Airport-Hotel Taxi Cab.

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A taxi cab driver moves between the airport A and two hotels B and C according to the following rules. If he is at the airport, he will be at one of the two hotels next with equal probability. If at a hotel, then he returns to the airport with probability 3/4 and goes to the other hotel with probability 1/4. (a) Find the transition matrix for the chain. (b) Suppose the driver begins at the airport at time 0. Find the probability for each of his three possible locations at time 2 and the probability he is at hotel B at time 3.
  1. Math and Tattoos
  2. stochastic processes
  3. probability
  4. markov chains
  5. markov processes
  6. airport
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