factory worker will quit with probability 1⁄2 during her first month, with probability 1⁄4 during her second month and with probability 1/8 each month after that. Whenever someone quits, their replacement will start at the beginning of the next month and follow the same pattern. Model this position’s status as a Markov chain. What is the long-run probability of having a new employee on a given month? please provide steps and explanations for answers

factory worker will quit with probability 1⁄2 during her first month, with probability 1⁄4 during her second month and with probability 1/8 each month after that. Whenever someone quits, their replacement will start at the beginning of the next month and follow the same pattern. Model this position’s status as a Markov chain. What is the long-run probability of having a new employee on a given month? please provide steps and explanations for answers

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. What states are absorbing states? b. Interpret the transition probabilities for a sophomore. c. Compute the probabilities that a sophomore will graduate and thata sophomore will drop out. d. In an address to the incoming class of 600 freshmen, the dean asksthe students to look around the auditorium and realize that about 50%of the freshmen present today will not make it to graduation day. Does your Markov process analysis support the dean’s statement? Explain. e. Currently, the college has 600 freshmen, 520 sophomores, 460 juniors, and 420 seniors. What percentage of the 2000 students attending thecollege will eventually graduate?
Anne and Barry take turns rolling a pair of dice, with Anne going first. Anne’s goal is to obtain a sum of 3, while Barry’s goal is to obtain a sum of 4. The game ends when either player reaches his goal,and the one reaching the goal is the winner. Define a Markov Chain to model the problem.
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ne bets $1. 0.45, he wins the game and with probability 1 - p = 0.55, he loses the game. His goal is to increase his capital to $3, and as soon as he does, the game is over. The game is also over if his capital is reduced to zero. Construct an absorbing Markov chain and answer the following questions. • What is the expected duration of the game? • What is the probability that he goes broke?
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
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Answer the following questions.
Alan and Betty play a series of games with Alan winning each game independently with probability p = 0.6. The overall winner is the first player to win two games in a row. Define a Markov chain to model the above problem.
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Given the following Markov Chain diagram. 0.15 On Duty Off 0.85 0.2 Duty 0.8 Given that you were on duty the first day (i.e., P(Day 1=On Duty) = 1 and P(Day %3D 1= Off Duty) = 0), answer the following questions. • What is the probability that you need to report towork on the 2mnd day (i.e., P(Day 2 = On Duty))? Answer: (Please write your answer with 2 decimal points) • What is the probability that you take a leave on the 2nd day (i.e., P(Day 2 = Off Duty))? Answer: (Please write your answer with 2 decimal points) • What is the probability that you go to work on the third day (i.e., P(Day 3=On Duty))? Answer: |(Please write your answer with 4 decimal points) • What is the probability that the third day was a Day Off (i.e., P(Day 3=Day Off)? Answer: (Please write your answer with 4 decimal points)