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 haulage company operates 3 depots – London, Sheffield and Brighton. The vehicles operated by the company can start or finish a journey at any of the depots. This being so, data has been obtained regarding weekly transitions and are represented by the following probabilities:- At present there are 10 vehicles in London, 10 in Sheffield and 15 in Brighton. Calculate how many would be expected to be in each depot in 3 weeks’ time? To From London Sheffield Brighton London 40 30 30 Sheffield 50 40 10 Brighton 40 30 30
13) THE MARKOV CHAIN EXPERIMENT DESCRIBED BELOW HAS TWO STATES: USING A CREDIT CARD AND NOT USING A CREDIT CARD. Hard HT A. GIVEN THE FIRST MONTH FIND THE PROBABILITIES FOR THE THIRD MONTH. P = Given month Card used Card not used B. FIND THE STEADY STABILIZE. Next month: Uses card .8 83 1.3 Card is not used (6 POINTS 14) GIV .2 7 Pr(a woman used a charge card) = .9 Pr(a woman did not use a charge card) = .1 A = [91] 211A STATE VECTOR WHERE THE PROBABILITIES
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A Southwest Energy Company pipeline has 3 safety shutoff valves in case the line springs a leak. These valves are designed to operate independently of one another. There is only a 7% chance that valve 1 will fail at any one time, a 10% failure chance for valve 2, and a 5% failure chance for valve 3. If there is a leak, find the following probabilities: that all 3 valves operate correctly.
Suppose that a basketball player’s success in free-throw shooting can be described with a Markov chain. If the player made the last free throw, then she is four times more likely to make the next free throw as miss it. If the player missed her last free throw, then she is equally likely to make or miss the next free throw. If she misses her first free throw, what is the probability she also misses her third and fifth free throw?
.A system is composed of 6 subsystems A, B, C , D, E, F as indicated in fig.1. If all of them function independently with probabilities P(A)=.9, P(B) =8, P(C) = .7 P(D) = P(E) = .5, and P(F) what is probability of successful system operation? P(F) = .5 B C .8 .9 .7 .5 .5 .5
Keystone puts a lot of work into showcasing properties to potential buyers (something like a personal open house). Each showcase results in either a ‘success’ (the buyer purchases the property) or a ‘failure’ (the buyer refuses to buy the property). Historically, Keystone figures that on any given showcase there is a 12% chance they will be successful and make a sale. Keystone has 6 showcases planned for this month, and they would like to explore some probabilities surrounding these showcases to help them manage this process and forecast revenues. In particular, Keystone wants to see at least two of these showcases turn into sales. What are the chances that exactly 2 of the showcases will result in a sale? What are the chances that they will make at least 3 sales? What are the chances that they will make fewer than 2 sales? Sometimes buyers will request a second viewing of the property. Based on historical evidence, buyers ask for a second viewing on 50% of successful showcases…
Pls help with below homework. Customer arrival follows a Poisson distribution. The rate is 1 job per day. The organization can process one customer per day at the beginning of the day. The organization holds 2 waiting rooms for customers. Therefore, in total there can't be more than 3 customers at the organization. (1 at service and 2 waiting). As a discrete-time Markov chain provide the transition probability matrix.
Appointments in a medical office are scheduled every 15 minutes. Throughout the day, appointments will be running on time or late, depending on the previous appointment only, according to the following matrix of transition probabilities: Previous Appointment Next Appointment On Time Late On Time .70 .30 Late .45 .55 What are the steady state probabilities?
Q2) In a language school, the path of a student's language level has been modeled as a Markov Chain with the following transition probabilities from the lowest level (Beginner) through the highest level (Advanced): Beginner Elementary Intermediate English Upper-Intermediate Quit Advanced Beginner Elementary Intermediate English Upper-Intermediate 0.4 0.1 0.05 0.45 0.1 0.5 0.3 0.1 0.1 0.4 0.3 0.2 0.2 0.4 0.2 0.2 Quit 1 Advanced Each student's state is observed at the beginning of each semester. For instance; if a student's language level is elementary at the beginning of the semester, there is an 30% chance that she will progress to intermediate level at the beginning of next semester, a 50% chance that she will still be in the elementary level, a 10% chance that she will regress to beginner level and 10% chance that she will quit the language school. Find the probability that a student with beginner level will eventually have an advanced level. Assume beginner level is state 1,…
Suppose 58.8% of small businesses experience cash flow problems in their first 5 years. A consultant takes a random sample of 557 businesses that have been opened for 5 years or less. What is the probability that greater than 55.85% of the businesses have experienced cash flow problems? Question 2 options: 1) 0.9214 2) 0.5000 3) -6.0341 4) 0.0786 5) >0.999
A certain television show airs weekly. Each time it airs, its ratings are categorized as "high," "average," or "low," and transitions between these categorizations each week behave like a Markov chain. If the ratings are high this week, they will be high, average, or low next week with probabilities 40%, 10%, and 50% respectively. If the ratings are average this week, they will be high, average, or low next week with probabilities 60%, 20%, and 20% respectively. If the ratings are low this week, they will be high, average, or low next week with probabilities 70%, 20%, and 10% respectively. Write all answers as integers or decimals. If the ratings are average this week, what is the probability that they will be low two weeks from now? If the ratings are average the first week, what is the probability that they will be low the second week? If the ratings are low the first week, what is the probability that they will be high the third week?