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a. A museum owns four paintings by Renoir, two by Cézanne, and three by Monet. It...

a. A museum owns four paintings by Renoir, two by Cézanne, and three by Monet. It has room to display only one of these paintings. Therefore, the painting on display is changed once a month. At that time, the painting on display is replaced by a randomly chosen one of the other eight paintings. Model this by a Markov chain with 3 states, the states determined by which artist is on display. What is the transition matrix?

b. If a painting by Renoir is on display now, how long will it be, on average, before a painting by Cézanne is on display?

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