Problem 2 Time to failure of each server is exponentially distributed with mean 0-10. Two servers are connected in a se- quential order (one after another). Assuming that the servers break down independently of one another find expected time before the (a) failure of the whole system. (b) How the result would change if the servers are connected in a parallel way?
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Please no written by hand solution
![Problem 2
Time to failure of each server is exponentially distributed with mean 0-10. Two servers are connected in a se-
quential order (one after another).
(a)
Assuming that the servers break down independently of one another find expected time before the
failure of the whole system.
(b)
How the result would change if the servers are connected in a parallel way?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe22b20f5-31a2-4874-a33a-f9e91abde40a%2F3f51cfbf-0307-4a6e-a5ea-c49fc1597056%2Fmeddzg9_processed.jpeg&w=3840&q=75)
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- Two computer specialists are completing work orders. The first specialist receives 60% of all orders. Each order takes her Exponential amount of time with parameter A₁ = 4 hours ¹. The second specialist receives the remaining 40% of orders. Each order takes him Exponential amount of time with parameter 2₂ = 5 hours-¹1 (a) A certain order was submitted to first specialist 10 minutes ago, and what is the probability that it is still not ready? (b) A certain order was submitted 10 minutes ago, and it is still not ready. What is the probability that the second specialist is working on it?6. A small company can employ 3 workers. Each worker independently stays on the job for an exponentially distributed time with a mean of one year and then quits. When a worker quits, it takes the company an exponentially distributed time with a mean of 1/10 of a year to hire a replacement for that worker (independently of how long it takes to replace other workers). If the company takes in $1000 per day in revenue when it has 3 workers, $800 per day when it has 2 workers, and $500 per day when it has 0 or 1 workers, what is the company's long-run average daily revenue?Suppose the customers arrive at a Poisson rate of on eper every 12 minutes, and that the service time is exponential at a rate of one service per 8 minutes. What are the average number of customers in the system(L) and the average time a customer spends in the system(W)?
- In a hypothetical city, there is a population of 200,000 people. During the year 2000, there were 1,000 deaths from all causes. All new cases of disease “X” have been accounted for and they total 600 (400 males and 200 females). During the year 2000 there were 120 deaths from disease “X”, 100 of them in males. Assume the number of existing cases of disease “X” at the end of 1999 is 1200. What is the prevalence rate of disease “X” per 100,000 population at the end of the year 2000?Suppose we have a small call center staffed by two operators A and B handling three telephone lines. A only handles line 1, and B only handles only line 2 and 3. Calls arrive according to a Poisson process with rate A = 100 calls per hour. All arrivals prefer line 1. Arrivals find all lines are busy will go away. Service times are exponentially distributed with a mean of 4 minutes. Customers are willing to wait an exponentially distributed length of time with a mean of 8 minutes before reneging if service has not begun. Describe a continuous time Markov chain to model the system and give the rate transition diagram and the generator G.There are 2 clerks in a college to receive dues from the students. If the service time for each student is exponential with mean 4 minutes, and the boys arrive in a Poisson fashion at the counter at the rate of 10/hour, what is the percentage of idle time for each clerk?.
- Suppose the customers arrive at a Poisson rate of on eper every 12 minutes, and that the service time is exponential at a rate of one service per 8 minutes. What are the average number of customers in the system(L) and the average time a customer spends in the system(W)? Now suppose that the arrival rate increases 20 percent.What is the corresponding change in L and W?Suppose we have a panel data of of 100 firms over 20 years at a monthly frequency. We are interested in how firms’ bond ratings affect their investment. Give an example of an omitted variable that can be fixed by Fixed Effects or First Differences. Give another example of an omitted variable that cannot be fixed by Fixed Effects or First DifferencesYou were asked to help with analysis of birth weights (BW) of 10,000 infants born in NYC during a certain period of time. The aim of the analysis is to see whether the birth weights of the infants are associated with mothers AGE at birth (continuous variable in years) and mothers smoking status (the maternal smoking status MSS contains 4 categories “Non-smoker”, “Past-smoker”, “Passive-smoker”, “Smoker”) and NYC boroughs (the BOROUGH variable contains 5 categories “Manhattan”, “Bronx”, “Brooklyn”, “Queens” and “State Island”). Write down the population model that will properly test the effect of 3-way interaction between AGE, MSS, and BOROUGH on BW. THIS IS A 3 WAY INTERACTION BETWEEN THIS THREE PREDICTORS. Attached is an example.
- You were asked to help with analysis of birth weights (BW) of 10,000 infants born in NYC during a certain period of time. The aim of the analysis is to see whether the birth weights of the infants are associated with mothers AGE at birth (continuous variable in years) and mothers smoking status (the maternal smoking status MSS contains 4 categories “Non-smoker”, “Past-smoker”, “Passive-smoker”, “Smoker”) and NYC boroughs (the BOROUGH variable contains 5 categories “Manhattan”, “Bronx”, “Brooklyn”, “Queens” and “State Island”). Write down the population model that assumes the effect of mother’s AGE at birth on infant weight BW is DIFFERENT for different levels of maternal smoking status (MSS) when adjusted for BOROUGH variable. Specify the name of each predictor in the model and/or what it means. Make sure that it is clear what each predictor means.You were asked to help with analysis of birth weights (BW) of 10,000 infants born in NYC during a certain period of time. The aim of the analysis is to see whether the birth weights of the infants are associated with mothers AGE at birth (continuous variable in years) and mothers smoking status (the maternal smoking status MSS contains 4 categories “Non-smoker”, “Past-smoker”, “Passive-smoker”, “Smoker”) and NYC boroughs (the BOROUGH variable contains 5 categories “Manhattan”, “Bronx”, “Brooklyn”, “Queens” and “State Island”). Write down the population model that will properly test the effect of 3-way interaction between AGE, MSS, and BOROUGH on BW.You were asked to help with analysis of birth weights (BW) of 10,000 infants born in NYC during a certain period of time. The aim of the analysis is to see whether the birth weights of the infants are associated with mothers AGE at birth (continuous variable in years) and mothers smoking status (the maternal smoking status MSS contains 4 categories “Non-smoker”, “Past-smoker”, “Passive-smoker”, “Smoker”) and NYC boroughs (the BOROUGH variable contains 5 categories “Manhattan”, “Bronx”, “Brooklyn”, “Queens” and “Staten Island”). Questions: 1) How many dummy variables do you need to create to analyze the effect of MSS? Select “Non-smokers” as a reference category. Write out all the dummy variables. 2)Write down the population model that estimates BW based on variables AGE and MSS. Make sure that it is clear what each predictor means. 3)How many parallel lines are computed by model from population model?
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