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. -/3 1 -/N 2 3 4 4 -14 5 (a) Calculate the total conductance at each vertex and the transition probabilities between each vertex. Write the transition matrix P. Find P⁰⁰. (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?

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. -/3 1 -/N 2 3 4 4 -14 5 (a) Calculate the total conductance at each vertex and the transition probabilities between each vertex. Write the transition matrix P. Find P⁰⁰. (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

Section: Chapter Questions

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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