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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.
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Is there sufficient evidence at the alpha =0.05 level to support the researcher's claim?
as the quality engineer for a small chain of fast food restaurants called mcdowells theyve got the big mac weve got the
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