A garage has 2 mechanics and 5 service bays to house vehicles. Customers arrive on averageevery 3 hours, and each mechanic works independently, taking an average of 2 hours to completea service (all times exponentially distributed). Vehicles that cannot find a free service bay leave.A. The garage is modeled as a Markov Chain with no distinction between service bays, i.e., statespace only tracks number of used bays (customers in garage). Draw the resultant statetransition diagram along with inter-state transition rates. How many states are there in total?

GivenThe number of mechanics in garage =2The number of service bays =5The average service time =2…

Answered: A garage has 2 mechanics and 5 service…

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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A coffee shop has two coffee machines, and only one coffee machine is in operation at any given time. A coffee machine may break down on any given day with probability 0.2 and it is impossible that both coffee machines break down on the same day. There is a repair store close to this coffee shop and it takes 2 days to fix the coffee machine completely. This repair store can only handle one broken coffee machine at a time. Define your own Markov chain and use it to compute the proportion of time in the long run that there is no coffee machine in operation in the coffee shop at the end of the day.
A computer store sells three types of microcomputers, brand A, brand B, and brand C. Of the computers they sell, 60% are brand A, 25% are brand B, and 15% are brand C. They have found that 20% of the brand A computers, 15% of the brand B computers, and 10% of brand C computers are returned for service during the warranty period. If a computer is returned for service during the warranty period, what is the probability that it is a brand A computer? A brand B computer? A brand C computer? The probability that it is a brand A computer is (Type a decimal. Round to three decimal places if needed.) The probability that it is a brand B computer is (Type a decimal. Round to three decimal places if needed.) The probability that it is a brand C computer is (Type a decimal. Round to three decimal places if needed.)
A bus containing 100 gamblers arrives in Las Vegas on a Monday morning. The gamblers play only poker or blackjack, and never change games during the day. The gamblers' daily choice of game can be modeled by a Markov chain: 95% of the gamblers playing poker today will play poker tomorrow, and 80% of the gamblers playing blackjack today will play blackjack tomorrow. (a) Write down the stochastic (Markov) matrix corresponding to this Markov chain. (b) If 60 gamblers play poker on Monday, how many gamblers play blackjack on Tuesday? (c) Find the unique steady-state vector for the Markov matrix in part (a).
↑ The 1990 census reported that 32% of the households in Middletown were homeowners and the remainder were renters. During the next decade, 10% of the homeowners became rent and the rest continued to be homeowners. Similarly, 14% of the renters became homeowners and the rest continued to rent (A) Fill in the appropriate transition matrix for this process. Homeowners Homeowners Renters Renters AR NE
Shakira's concerts behave like a Markov chain. If the current concert gets cancelled, then there is an 90% chance that the next concert will be cancelled also. However, if the current concert does not get cancelled, then there is only a 50% chance that the next concert will be cancelled. What is the long-run probability that a concert will not be cancelled? a. 1/4 b. 1/10 c. 1/6 d. 1/2 e. 5/6 f. None of the others are correct
The main topic is Markov Chains:Students in Geology class never know what is going to happen in the class, as the teacher may: give them a pop quiz, take them to field practice, analyze the topic of the day, or lecture on a special topic.If one day there is a test, the next day there is always a field practice.If one day there is field practice, the next day there is no practice or test, but there is still a chance of the day's topic or special lecture.of the day or of the special lecture.If on a certain day the topic is tested, the probabilities for the next day are ¼ for the test, 1/6 for the topic and 1/3 for the lecture.and 1/3 for the lecture.If one day there is a lecture, the odds for the next day are ¼ for the test, 1/8 for the practice, 1/8 for the topic analysis and ½ for the lecture.for the analysis of the topic and ½ for the lecture.One of the students has calculated that they can expect quizzes 43/287 of the lecture days; field practice72/287 of the class days; topic…
solve using Markov Chain
In any given day the air quality in a certain city is either good or bad. Records show that when the air quality is good on one day, then there is a 95% chance that it will be good the next day, and when the air quality is bad on one day, then there is 45% chance it will be bad the next day. a. Give the transition matrix. b. if the air quality is good today, what is the probability it will be good two days from now? c. if the air quality is bad today, what is the probability it will be bad three days from now? d. if the there is 20% chance the air quality is good today, what is the probability it will be good tomorrow?
I conduct an online study to determine whether rewards reduce procrastination. All participants are asked to complete a task sometime before a deadline (10 days from now). The computer randomly assigns participants to one of three groups, and emails them their instructions; one group receives a reward as soon as they do the task (contingent reward); a second group receives rewards as soon as they finish the task as long as it is before the deadline (non-contingent reward) and the third group does not receive rewards at all (no reward). Three participants in the no reward condition do not complete the task, and so are dropped from analyses. The dependent variable is the amount of time (in days) it takes participants to complete the task. The JAMOVI output is attached. Post-hoc Tukey tests show that... (select all that apply) ANOVA ANOVA - Time Reward Residuals Assumption Checks Homogeneity of Variances Test (Levene's) F df1 df2 0.056 Statistic 0.964 Sum of Squares df Mean Square F…

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