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Unformatted text preview: ) with probability 0.6.
When he misses he is more conservative the next time and hits (H) with probability 0.7, misses (M) with probability 0.3. (a) Write the transition probability
for the two state Markov chain with state space {H, M }. (b) Find the longrun
fraction of time he hits a shot.
1.26. Folk wisdom holds that in Ithaca in the summer it rains 1/3 of the time,
but a rainy day is followed by a second one with probability 1/2. Suppose that
Ithaca weather is a Markov chain. What is its transition probability?
Chains with three or more states
1.27. (a) Suppose brands A and B have consumer loyalties of .7 and .8, meaning
that a customer who buys A one week will with probability .7 buy it again the
next week, or try the other brand with .3. What is the limiting market share for
each of these products? (b) Suppose now there is a third brand with loyalty .9,
and that a consumer who changes brands picks one of the other two at random.
What is the new limiting market share for these three pr...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).
 Spring '10
 DURRETT
 The Land

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