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. 3 4 -IN 2 1 3 4 4 th 5 (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?
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. 3 4 -IN 2 1 3 4 4 th 5 (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?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text: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.
3
4
-IN
2
1
3
4
4
th
5
(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?
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