Each week a student can be either up-to-date or behind. If the student is up-to- date, then the probability of staying up to date is 0.8, otherwise the student falls behind. If the student is behind, then the student will be up-to-date next week with probability 0.6. n-step transition matrix 8.21 .4] r₁j (1) = [8 2 2
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![Each week a student can be either up-to-date or behind. If the student is up-to-
date, then the probability of staying up to date is 0.8, otherwise the student falls
behind. If the student is behind, then the student will be up-to-date next week
with probability 0.6.
n-step transition matrix
rij (1) = [.8
2
.4]
O
0.6×0.8+.2×
и](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5878d19f-0223-4d85-98f6-0dd2260b83d4%2Fcb4e7a70-05f7-4726-8c8c-c01cde6db453%2Fw131kyj_processed.png&w=3840&q=75)
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- Suppose that Phone A has a 20% market share initially, with Phone B having an 80% market share. The transition matrix to the right represents customers who currently own phones A and B and the probability that they will upgrade to a new phone A or B. Use this transition matrix to find the share for each phone after the following upgrades. A B A 0.8 0.2 B 0.25 0.75 (a) First upgrade (b) Second upgrade (c) Third upgrade (a) With the first upgrade, Phone A has % of the market and Phone B has % of the market. (Round your answers to two decimal places as needed.)Determine if P = .8 .2 1 is a regular stochastic matrix.An average of 100 customers per hour arrive at GothamCity Bank. It takes a teller an average of 2 minutes to servea customer. Interarrival and service times are exponential.The bank currently has four tellers working. The bankmanager wants to compare the following two systems withregard to average number of customers present in the bankand the probability that a customer will spend more than 8minutes in the bank:System 1 Each teller has her own line, and no jockeyingbetween lines is permitted.System 2 All customers wait in a single line for the firstavailable teller.If you were the bank manager, which system would youprefer?
- 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?A piece of equipment will function only when the three components A, B and C are working. The probability of A failing during one year is 0.15, that of B failing is 0.05, and that of C failing is 0.10. What is the probability that the equipment will fail before the end of the year?Which of the transition matrices are regular? Select all that apply: A = [0.5 0.5 E = 0.6 0.4 O B 0.3 0.7] %3= 0.2 0.8 OD= 0.7 0.3
- EXAMPLE 6.38 Consider an M/M/c queueing system. Find the probability arriving customer is forced to join queue. that anIn an office complex of 1100 employees, on any given day some are at work and the rest are absent. It is known that if an employee is at work today, there is an 80% chance that she will be at work tomorrow, and if the employee is absent today, there is a 51% chance that she will be absent tomorrow. Suppose that today there are 913 employees at work. .80 .49 ( a) Find the transition matrix for this scenario. .2 .51 (b) Predict the number that will be at work five days from now. 781.5 2.45 (c) Find the steady-state vector. .29EXAMPLE 6.67 If λ = 2 per hour and = 3 per hour in an M/M/4/N queueing system and there are 2 chairs for waiting customers, calculate the probability that there are 7 customers in the system.
- Show all work clearly. A powerplant’s daily electricity generation is managed by identical control systems that operate in parallel. Each control system can fail, during the day, with probability 1−p independently of other control systems. The powerplant can generate electricity successfully during a day if at least 50 percent of its control systems remain operative. For what values of p having a powerplant with four control systems is more preferable to a powerplant with two control systems?When the store opens, Arish, Meera, and Zenobia enter. There are two service counters. Arish begins service at one counter, and Meera begins service at the other counter. Zenobia waits until either Arish or Meera finishes service, and then begins service at that point in time. Assume that the three service times are independent, exponentially distributed random variables. Arish's service time has mean 4 minutes, Meera's service time has mean 5 minutes, and Zenobia's service time has mean 6 minutes. (a) What is the probability that Arish completes service before Meera? (b) What is the expected time that Zenobia waits until starting service? (C) What is the probability that the three finish in alphabetical order?the map below shows a one-way subway system starting from station 1. A passenger can go from each station to others with equal probability. so a passenger from station 1 can go any other station with probability of 1/4 since there are 14 remaining stationss. a passenger from station 11 can go to any of the remaining stations (12-15) with probability 1/4. what is the probability transition matrix?
