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Markov Chain Calculations Consider the Markov model with transition probabilities P(St+1 St) represented using the state transition diagram below. 20% a 60% 80% 20% C b 70% 20% 30% (a) Write the state-transition probabilities as a 3x3 matrix M in which Ma,b= P(bla). (b) If the state is initially a (i.e., P(S₁ = a) = 1), what is P(S3 = a)? (c) What is the stationary distribution of this Markov model?

Markov Chain Calculations Consider the Markov model with transition probabilities P(St+1 St) represented using the state transition diagram below. 20% a 60% 80% 20% C b 70% 20% 30% (a) Write the state-transition probabilities as a 3x3 matrix M in which Ma,b= P(bla). (b) If the state is initially a (i.e., P(S₁ = a) = 1), what is P(S3 = a)? (c) What is the stationary distribution of this Markov model?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Transcription: 4. **Markov Chain Calculations** Consider the Markov model with transition probabilities \( P(S_{t+1}|S_t) \) represented using the state transition diagram below. Diagram Explanation: - The diagram consists of three states: \( a \), \( b \), and \( c \). - Arrows represent transitions between states, annotated with the probability of each transition. Transitions: - \( a \) to \( a \): 20% - \( a \) to \( b \): 80% - \( b \) to \( a \): 20% - \( b \) to \( b \): 20% - \( b \) to \( c \): 60% - \( c \) to \( c \): 70% - \( c \) to \( a \): 30% Tasks: (a) Write the state-transition probabilities as a 3x3 matrix \( M \) in which \( M_{a,b} = P(b|a) \). (b) If the state is initially \( a \) (i.e., \( P(S_1 = a) = 1 \)), what is \( P(S_3 = a) \)? (c) What is the stationary distribution of this Markov model?
Transcribed Image Text:Transcription: 4. **Markov Chain Calculations** Consider the Markov model with transition probabilities \( P(S_{t+1}|S_t) \) represented using the state transition diagram below. Diagram Explanation: - The diagram consists of three states: \( a \), \( b \), and \( c \). - Arrows represent transitions between states, annotated with the probability of each transition. Transitions: - \( a \) to \( a \): 20% - \( a \) to \( b \): 80% - \( b \) to \( a \): 20% - \( b \) to \( b \): 20% - \( b \) to \( c \): 60% - \( c \) to \( c \): 70% - \( c \) to \( a \): 30% Tasks: (a) Write the state-transition probabilities as a 3x3 matrix \( M \) in which \( M_{a,b} = P(b|a) \). (b) If the state is initially \( a \) (i.e., \( P(S_1 = a) = 1 \)), what is \( P(S_3 = a) \)? (c) What is the stationary distribution of this Markov model?
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