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3. Consider a random walk on the graph with 6 vertices below. Suppose that 0 and 5 are absorbing vertices, but the random walker is more strongly attracted to 5 than to 0. So for each turn, the probability that the walker moves right is 0.7, while the probability he moves left is only 0.3. 2 3 (a) Write the transition matrix P for this Markov process. (b) Find POO. 4 S (c) What is the probability that a walker starting at vertex 1 is absorbed by vertex 0? (d) What is the probability that a walker starting at vertex 1 is absorbed by vertex 5? (e) What is the probability that a walker starting at vertex 4 is absorbed by vertex 5? (f) What is the probability that a walker starting at vertex 3 is absorbed by vertex 5? (g)What is the expected number of times that a walker starting at vertex 1 will visit vertex 2? (h) What is the expected number of times that a walker starting at vertex 1 will visit vertex 4?

3. Consider a random walk on the graph with 6 vertices below. Suppose that 0 and 5 are absorbing vertices, but the random walker is more strongly attracted to 5 than to 0. So for each turn, the probability that the walker moves right is 0.7, while the probability he moves left is only 0.3. 2 3 (a) Write the transition matrix P for this Markov process. (b) Find POO. 4 S (c) What is the probability that a walker starting at vertex 1 is absorbed by vertex 0? (d) What is the probability that a walker starting at vertex 1 is absorbed by vertex 5? (e) What is the probability that a walker starting at vertex 4 is absorbed by vertex 5? (f) What is the probability that a walker starting at vertex 3 is absorbed by vertex 5? (g)What is the expected number of times that a walker starting at vertex 1 will visit vertex 2? (h) What is the expected number of times that a walker starting at vertex 1 will visit vertex 4?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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4. Consider the graph with 6 vertices given below and with resistances given by the numbers above each edge. As before, vertices 0 and 5 are absorbing. 1 -IN 2 1 4 4 -14 (a) Calculate the total conductance at each vertex and the transition probabilities between each vertex. Write the transition matrix P. Find Poo. (b) What is the probability that a walker starting at vertex 1 is absorbed by vertex 0? (c) What is the probability that a walker starting at vertex 3 is absorbed by vertex 5? (d) What is the expected number of times that a walker starting at vertex 1 will visit vertex 2?
Transcribed Image Text:4. Consider the graph with 6 vertices given below and with resistances given by the numbers above each edge. As before, vertices 0 and 5 are absorbing. 1 -IN 2 1 4 4 -14 (a) Calculate the total conductance at each vertex and the transition probabilities between each vertex. Write the transition matrix P. Find Poo. (b) What is the probability that a walker starting at vertex 1 is absorbed by vertex 0? (c) What is the probability that a walker starting at vertex 3 is absorbed by vertex 5? (d) What is the expected number of times that a walker starting at vertex 1 will visit vertex 2?
3. Consider a random walk on the graph with 6 vertices below. Suppose that 0 and 5 are absorbing vertices, but the random walker is more strongly attracted to 5 than to 0. So for each turn, the probability that the walker moves right is 0.7, while the probability he moves left is only 0.3. 2 3 (a) Write the transition matrix P for this Markov process. (b) Find POO. 4 5 (c) What is the probability that a walker starting at vertex 1 is absorbed by vertex 0? (d) What is the probability that a walker starting at vertex 1 is absorbed by vertex 5? (e) What is the probability that a walker starting at vertex 4 is absorbed by vertex 5? (f) What is the probability that a walker starting at vertex 3 is absorbed by vertex 5? (g)What is the expected number of times that a walker starting at vertex 1 will visit vertex 2? (h) What is the expected number of times that a walker starting at vertex 1 will visit vertex 4?
Transcribed Image Text:3. Consider a random walk on the graph with 6 vertices below. Suppose that 0 and 5 are absorbing vertices, but the random walker is more strongly attracted to 5 than to 0. So for each turn, the probability that the walker moves right is 0.7, while the probability he moves left is only 0.3. 2 3 (a) Write the transition matrix P for this Markov process. (b) Find POO. 4 5 (c) What is the probability that a walker starting at vertex 1 is absorbed by vertex 0? (d) What is the probability that a walker starting at vertex 1 is absorbed by vertex 5? (e) What is the probability that a walker starting at vertex 4 is absorbed by vertex 5? (f) What is the probability that a walker starting at vertex 3 is absorbed by vertex 5? (g)What is the expected number of times that a walker starting at vertex 1 will visit vertex 2? (h) What is the expected number of times that a walker starting at vertex 1 will visit vertex 4?
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