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[9] Markov chains can be used to model the voting behavior. Suppose the U.S. pop- ulation of voters are distributed between Democratic (D), Republican (R), and Independent (I) parties. Suppose that transition probabilities between parties can be represented as in the following diagram (ignore non-participation) R 0.2 0.1 D

[9] Markov chains can be used to model the voting behavior. Suppose the U.S. pop- ulation of voters are distributed between Democratic (D), Republican (R), and Independent (I) parties. Suppose that transition probabilities between parties can be represented as in the following diagram (ignore non-participation) R 0.2 0.1 D

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.5: Markov Chain
Problem 55E
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[9] Markov chains can be used to model the voting behavior. Suppose the U.S. pop- ulation of voters are distributed between Democratic (D), Republican (R), and Independent (I) parties. Suppose that transition probabilities between parties can be represented as in the following diagram (ignore non-participation) R 0.3 0.1 0.2 0.1 0.3 0.1 a) Write down the corresponding Markov chain model. In particular, write down the state vector and transition matrix explicitly. b) Suppose that somehow the transition probability from D to R is expected to rise to 0.25 from 0.20, and the transition probability from D to D remains the same. Describe qualitatively, how Democratic, Republican and Independent votes will evolve until the new stationary distribution is reached.
Transcribed Image Text:[9] Markov chains can be used to model the voting behavior. Suppose the U.S. pop- ulation of voters are distributed between Democratic (D), Republican (R), and Independent (I) parties. Suppose that transition probabilities between parties can be represented as in the following diagram (ignore non-participation) R 0.3 0.1 0.2 0.1 0.3 0.1 a) Write down the corresponding Markov chain model. In particular, write down the state vector and transition matrix explicitly. b) Suppose that somehow the transition probability from D to R is expected to rise to 0.25 from 0.20, and the transition probability from D to D remains the same. Describe qualitatively, how Democratic, Republican and Independent votes will evolve until the new stationary distribution is reached.
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