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3 Consider the following transition matrix: [00100 01 000001 P = 0000 1 0 000 000 0 100 0000 a Which states are transient? b Which states are recurrent? 21/m

3 Consider the following transition matrix: [00100 01 000001 P = 0000 1 0 000 000 0 100 0000 a Which states are transient? b Which states are recurrent? 21/m

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 49E: Consider the Markov chain whose matrix of transition probabilities P is given in Example 7b. Show...
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Please resolve question 3 and parts please
PROBLEMS Group A 1 In Example 1, what is the period of states 1 and 3? 2 Is the Markov chain of Section 17.3, Problem 1, an ergodic Markov cham? 3 Consider the following transition matrix: [0 0 1 0 0 0 000001 000010 1 1 0 0 0 100000 0000/ 4 P = a Which states are transient? b Which states are recurrent? .4 0 .6 P₁.3 .3 .4 0 5.5 P₂ = 0 0.3] .2 .2 .4 .2 .6 .1 .1 .2 L.2 0 0.8] [.7 c d Identify all closed sets of states. Is this chain ergodic? 4 For each of the following chains, determine whether the Markov chain is ergodic. Also, for each chain, determine the recurrent, transient, and absorbing states. [.2 .8 0 01 0 09.1 4.5.1 .1 0 0 0 0 1. 5 Fifty-four players (including Gabe Kaplan and James Garner) participated in the 1980 World Series of Poker. Bach player began with $10,000. Play continued until one payer had won everybody else's money. If the World Series of Poker were to be modeled as a Markov chain, how many absorbing states would the chain have? 6 Which of the following chains is ergodic? 0.8 2 P₁ = .3 .7 0 4 5 1 P₂ =
Transcribed Image Text:PROBLEMS Group A 1 In Example 1, what is the period of states 1 and 3? 2 Is the Markov chain of Section 17.3, Problem 1, an ergodic Markov cham? 3 Consider the following transition matrix: [0 0 1 0 0 0 000001 000010 1 1 0 0 0 100000 0000/ 4 P = a Which states are transient? b Which states are recurrent? .4 0 .6 P₁.3 .3 .4 0 5.5 P₂ = 0 0.3] .2 .2 .4 .2 .6 .1 .1 .2 L.2 0 0.8] [.7 c d Identify all closed sets of states. Is this chain ergodic? 4 For each of the following chains, determine whether the Markov chain is ergodic. Also, for each chain, determine the recurrent, transient, and absorbing states. [.2 .8 0 01 0 09.1 4.5.1 .1 0 0 0 0 1. 5 Fifty-four players (including Gabe Kaplan and James Garner) participated in the 1980 World Series of Poker. Bach player began with $10,000. Play continued until one payer had won everybody else's money. If the World Series of Poker were to be modeled as a Markov chain, how many absorbing states would the chain have? 6 Which of the following chains is ergodic? 0.8 2 P₁ = .3 .7 0 4 5 1 P₂ =
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