7.40. A random walk on a graph goes from vertex to adjacent vertex by walkingalong the connecting edge. It chooses the edge at random: all edges connecting tothat vertex are equally likely. Consider a random walk on the graph below.(a) Find the long-term proportion of time spent at vertex 0.(b) Find the expected return time to 0.(c) Find the probability that a random walk from vertex e hits 0 before hittingeither a or b.(d) Suppose the random walk starts at 0. Find the expected time to reach{a Ub}.[Hint: Make use of symmetry!]A

References Rahman, M. S. (2017). Basic graph theory (Vol. 9). India: Springer.

Answered: 7.40. A random walk on a graph goes…

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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stion 3 of 14 <. You and a group of friends are going to a five-day outdoor music festival during spring break. You hope it does not rain during the festival, but the weather forecast says there is a 45% chance of rain on the first day, a 55% chance of rain on the second day, a 10% chance of rain on the third day, a 10% chance of rain on the fourth day, and a 5% chance of rain on the fifth day. Assume these probabilities are independent of whether it rained on the previous day or not. What is the probability that it does not rain during the entire festival? Express your answer as a percentage to two decimal places.
Tip at least 20% Tip less than 20% Works or worked in service industry 22 5 Never worked in service industry 36 8 Find P(individual has worked a service industry job) (2) Find P(individual either has never worked in the service industry or tips less than 20%) (4) Find P(individual has never worked in the service industry and tips less than 20%) (4) Find P(Tipping at least 20% | Service industry worker) (4) Find P(Two people both tip at least 20%)
Show work for every step. Two types of customers (Preferred and Regular) call a service center. Preferred customers call with rate 3 per hour, and Regular customers call with rate 5 per hour. The interarrival times of the calls for each customer type are exponentially distributed. If the call center opens at 8:00 AM, what is the probability that the first call (regardless of customers type who calls) is received before 8:15 AM?
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Frozen computer: A computer system administrator noticed that computers running a particular operating system seem to freeze up more often as the installation of the operating system ages. She measures the time (in minutes) before freeze-up for 6 computers one month after installation and for 6 computers seven months after installation. The results are shown. Can you conclude that the time to freeze-up is more variable in the seventh month than the first month after installation? Let σ1 denote the variability in time to freeze-up in the first month after installation. Use the α=0.10 level and the critical value method with the table. One month: 207.4 233.1 215.9 235.1 225.6 244.4 Seven months: 84.3 53.2 127.3 201.3 174.2 246.2 State the null and alternate hypothesis

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