1 consider the markov chain with transition matrix12 12, Ask an Expert

Statistics

1. Consider the Markov chain with transition matrix

1/2 1/2 P = 1/4 3/4.

Find the fundamental matrix Z for this chain. Compute the mean first passage matrix using Z.

2. A study of the strengths of Ivy League football teams shows that if a school has a strong team one year it is equally likely to have a strong team or average team next year; if it has an average team, half the time it is average next year, and if it changes it is just as likely to become strong as weak; if it is weak it has 2/3 probability of remaining so and 1/3 of becoming average.

(a) A school has a strong team. On the average, how long will it be before it has another strong team?

(b) A school has a weak team; how long (on the average) must the alumni wait for a strong team?

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