The transition matrix for a Markov process is
and the initial-state distribution
Find
To find:
The vector
Answer to Problem 1BMO
Solution:
The vector
Explanation of Solution
Given:
The transition matrix for a Markov process is
and the initial-state distribution vector is
Approach:
From the given data,
Write the expression of the probability distribution after one observation
Write the expression of the probability distribution after two observations
Calculation:
Substitute
Similarly, Substitute
Conclusion:
Hence, vector
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Chapter 9 Solutions
Finite Mathematics for the Managerial, Life, and Social Sciences
- Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.arrow_forwardConsider the Markov chain whose matrix of transition probabilities P is given in Example 7b. Show that the steady state matrix X depends on the initial state matrix X0 by finding X for each X0. X0=[0.250.250.250.25] b X0=[0.250.250.400.10] Example 7 Finding Steady State Matrices of Absorbing Markov Chains Find the steady state matrix X of each absorbing Markov chain with matrix of transition probabilities P. b.P=[0.500.200.210.300.100.400.200.11]arrow_forward12. Robots have been programmed to traverse the maze shown in Figure 3.28 and at each junction randomly choose which way to go. Figure 3.28 (a) Construct the transition matrix for the Markov chain that models this situation. (b) Suppose we start with 15 robots at each junction. Find the steady state distribution of robots. (Assume that it takes each robot the same amount of time to travel between two adjacent junctions.)arrow_forward
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