1. On a given day, a retired English professor, Dr. Charles Fish, amuses himself with only one of the following activities: reading (activity 1), gardening (activity 2), or working on his book about a river valley (activity 3). For 1 ≤ i ≤ 3, let Xn = i if Dr. Fish devotes day n to activity i. Suppose that {Xn : n = 1, 2, . . .} is a Markov chain, and depending on which of these activities he chooses on a certain day, the probability of engagement in any one of the activities on the next day is given by the transition probability matrix

Find the proportion of days Dr. Fish devotes to each activity.

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0.30 0.25 0.45) P=0.40 0.10 0.50 0.25 0.40 0.35