/4 0 A Markov chain X (0), X(1), X(2),... has the transition state diagram shown below....
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¹/4 0 A Markov chain X (0), X(1), X(2),... has the transition state diagram shown below. ¹/3 ²/5 5/12 1 2 3/10 3 4 ¹/5 The diagram above shows all possible transitions, but not all transition probabilities are labelled. (a) Write down the transition probability matrix P for the Markov chain. Given that the Markov chain is initially in state 4: (b) Use matrix multiplication to find the probability mass function for X (2). Show your working and give your answers as fractions. (c) What is the probability that the Markov chain has reached an absorbing state by step 2? (d) What is the probability that the Markov chain has not reached an absorbing state by step 2, but reaches an absorbing state by step 3? Give your answer as a fraction. Hint: a tree diagram might be helpful. Activate Window Go to Settings to acti (e) Does E(X(n)) remain constant for this Markov chain? Justify your answer (in 2-3 lines only). ¹/4 0 A Markov chain X (0), X(1), X(2),... has the transition state diagram shown below. ¹/3 ²/5 5/12 1 2 3/10 3 4 ¹/5 The diagram above shows all possible transitions, but not all transition probabilities are labelled. (a) Write down the transition probability matrix P for the Markov chain. Given that the Markov chain is initially in state 4: (b) Use matrix multiplication to find the probability mass function for X (2). Show your working and give your answers as fractions. (c) What is the probability that the Markov chain has reached an absorbing state by step 2? (d) What is the probability that the Markov chain has not reached an absorbing state by step 2, but reaches an absorbing state by step 3? Give your answer as a fraction. Hint: a tree diagram might be helpful. Activate Window Go to Settings to acti (e) Does E(X(n)) remain constant for this Markov chain? Justify your answer (in 2-3 lines only).
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Answer rating: 100% (QA)
a The transition probability matrix P for the Markov chain is as follows P 23 13 0 0 12 14 14 0 0 12 310 512 0 0 1 0 b To find the probability mass function for X2 given that the Markov chain is initi... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
Posted Date:
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