The weather at a seaside resort each day is classified as either Sunny or Rainy. The probability that any two consecutive days are both sunny is 0.6, with the other three combinations being equally likely. Treating the situation as a two-state Markov chain, answer the following: (a) Find the transition matrix P and the stationary distribution vector r. (b) Find the 5-step transition matrix p(5) and hence find the probability that, if it is sunny on Sunday, it will be rainy on Friday. (c) If a day is chosen at random and found to be rainy, what is the expected number of sunny days before the next rainy day?

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