3. Consider the Markov chain with three states, S={1,2,3}, that has the following transition matrixYAP=/3a. Draw the state transition diagram for this chain.If we know P(X1=1)=P(X1=2)=1/4, find P(X1=3, X2=2,X3=1)

Consider the Markov chain with three states, S={1,2,3}, that has the following transition matrix ½ 4 Y4 P= Draw the state transition diagram for this chain. If we know P(X1=1)=P(X1=2)=1/4, find P(X1=3, X2=2,X3=1)

Consider the Markov chain with three states, S={1,2,3}, that has the following transition matrix ½ 4 Y4 P= Draw the state transition diagram for this chain. If we know P(X1=1)=P(X1=2)=1/4, find P(X1=3, X2=2,X3=1)

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter17: Markov Chains

Section17.5: Steady-state Probabilities And Mean First Passage Times

Problem 3P

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Question

3. Consider the Markov chain with three states, S={1,2,3}, that has the following transition matrix
YA
P=
/3
a. Draw the state transition diagram for this chain.
If we know P(X1=1)=P(X1=2)=1/4, find P(X1=3, X2=2,X3=1)

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Consider the Markov chain with three states,S={1,2,3}, that has the following transition matrix p= 1/2 1/4 1/4 1/3 0 2/3 1/4 1/2 0 a. Draw the state transition diagram for this chain b. If we know P(X1=1) =P(X1=2) =1/4, find P(X1=3, X2=2,X3=1)
3. Consider the Markov chain with three states, S={1,2,3}, that has the following transition matrix P= a. Draw the state transition diagram for this chain. (10 marks) b. If we know P(Xi=1)=P(X1=2)=1/4, find P(X1=3, X2=2,X3=1) (10 marks)
1. Consider a Continuous Time Markov chain with state space S = {1, 2, 3} and with instantaneous transition rates of: 921 = .5 931 =0 912 = 1.2 932 = 0 913 = .6 923 = .2 Find Tj j= 1, 2, 3. Repeat with q31 = .5.
The question is attached.
For systems with n components, the number of states in a non-simplified Markov chain is as follows: Each part may be in one of two states: working or broken.
The number of states in non-simplified Markov chains for systems with n members is as follows: Each component may be in one of two states: failing or working.
Consider again the Grasshopper Markov Chain from Chapter 4b, with a state variable S = {-4,-3, -2,-1,0, +1, +2, +3, +4} and with the grasshopper known to start in position 0: P(S) = [0,0,0,0,1,0,0,0,0]: 0.75 0.25 0.5 0.25 0.5 Select one: True False 0.25 0.5 -3 NTS LINK - 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.75 Let's turn this into a Hidden Markov Model by assuming that we cannot see the grasshopper, but we hear it chirping (observation variable Chirp(C)), with the sound coming from the left, the center, or the right (Val(C) = {1, c,r)). Suppose we have the following observation model: 0.5 1 The backward message b) [1/9, 1/9, 1/9, 1/9, 1/9, 1/9, 1/9, 1/9, 1/91 #C 2 ( -1 0 11 1 -3 ( 0.25 P(CS) T 0 10 0 r 0 0 0 1 1 1 0.25 0.5 1 0.25 0.5 0.25 Finally, suppose we have an observation sequence of Chirp observations of length 7. Which of the following sentences are correct:
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