3. (a) A Markov process with 2 states is used to model the weather in a certain town. State 1 corresponds to a sunny day. State 2 corresponds to a rainy day. The transition matrix for this Markov process is [0.7 0.4] P = 0.3 0.6 %3D (i) If today is rainy, what is the probability that tomorrow will be sunny? (ii) Find the steady state probability vector. (iii) In the long run, how many days a week are sunny?

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