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1. A ?ea moves around the vertices of a triangle in the following manner: Whenever it is at vertex i it moves to its clockwise neighbor vertex with probability pi and to the counterclockwise neighbor with probability qi = 1 - pi , i = 1, 2, 3.
(a) Find the proportion of time that the ?ea is at each of the vertices.
(b) How often does the ?ea make a counterclockwise move that is then followed by ?ve consecutive clockwise moves?
2. Consider a Markov chain with states 0, 1, 2, 3, 4. Suppose P0,4 = 1; and suppose that when the chain is in state i, i > 0, the next state is equally likely to be any of the states 0, 1, ... , i - 1. Find the limiting probabilities of this Markov chain.
"If you took 40 employees at random from the corporation, there is a pretty good chance the average number of days absent would be 12 or more. That's what happened to us-chance variation." Is this a good defense? Justify your answer.
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