An absorbing Markov Chain has 5 states where states #1 and #2 are absorbing states and the following transition probabilities are known: p3,2=0.1, p3, 3=0.4, p3,5=0.5 p4,1=0.1, p4,3=0.5, ...
An absorbing Markov Chain has 5 states where states #1 and #2 are absorbing states and the following transition probabilities are known:
p3,2=0.1, p3, 3=0.4,
p3,5=0.5
p4,1=0.1, p4,3=0.5,
p4,4=0.4
p5,1=0.3,
p5,2=0.2,
p5,4=0.3, p5,5 = 0.2
(a) Let T denote the transition matrix. Compute T3.
Find the probability that if you start in state #3 you will be in
state #5 after 3 steps.
(b) Compute the matrix N = (I - Q)-1. Find the expected
value for the number of steps prior to hitting an absorbing state
if you start in state #3. (Hint: This will be the sum of one of the
rows of N.)
steps
(c) Compute the matrix B = NR. Determine the probability that you
eventually wind up in state #1 if you start in state #4.
Homework Answers
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An absorbing Markov Chain has 5 states where states #1 and #2 are absorbing states and the following transition probabilities are known: p3,2=0.1, p3, 3=0.4, p3,5=0.5 p4,1=0.1, p4,3=0.5, ...
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T is the transition matrix for a 4-state absorbing Markov Chain. State 1 and state #2 are absorbing states. 1 0 00 0 0 0.45 0.05 0.5 1 0 0 0.15 0 0.5 0.35 Use the standard methods for absorbing Markov Chains to find the matrices N (I Q)1 and BNR. Answer the following questions based on these matrices. (Give your answers correct to 2 decimal places.) a If you start n state #3, what is the expected number of...
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