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Unformatted text preview: , Helen, Joni, Mark, Sam, and Tony) play catch. If
Dick has the ball he is equally likely to throw it to Helen, Mark, Sam, and
Tony. If Helen has the ball she is equally likely to throw it to Dick, Joni, Sam,
and Tony. If Sam has the ball he is equally likely to throw it to Dick, Helen,
Mark, and Tony. If either Joni or Tony gets the ball, they keep throwing it to 73 1.12. EXERCISES each other. If Mark gets the ball he runs away with it. (a) Find the transition
probability and classify the states of the chain. (b) Suppose Dick has the ball
at the beginning of the game. What is the probability Mark will end up with
1.59. Use the second solution in Example 1.48 to compute the expected waiting
times for the patterns HHH , HHT , HT T , and HT H . Which pattern has the
longest waiting time? Which ones achieve the minimum value of 8?
1.60. Sucker bet. Consider the following gambling game. Player 1 picks a three
coin pattern (for example HT H ) and player 2 picks another (say T HH ). A coin
is ﬂipped repeatedly and outcomes are recorded until one of the two patter...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).
- Spring '10
- The Land