Compute three step transition probability and long run behavior of transit system markov chain.

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A rapid transit system has just started operating. In the first month of operation, it was found that 25 % of commuters are using the system while 75 % are travelling by automobile. Suppose that each month 10 % of transit users go back to using their cars, while 30 % of automobile users switch to the transit system. (a) Compute the three step transition probability p3. (b) What will be the fractions using rapid transit in the fourth month? (c) In the long run?
  1. Math and Tattoos
  2. markov
  3. stochastic processes
  4. transit system
  5. probability
  6. three step transition matrix
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I think you need to find P^4. Since q1=q0P, , .... q4=q0P^4

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