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Suppose that the space shuttle has three separate computer control systems: the main system and two backup duplicates of it. The first backup would monitor the main system and kick in if the main system failed. Similarly, the second backup would monitor the first. We can assume that the failure of one system is independent of the failure of another system, since the systems are separate. The probability of failure for any one system on any one mission is known to be 0.01.
a. Find the probability that the shuttle is left with no computer control system on a mission.
b. How many backup systems does the space shuttle need if the probability that the shuttle is left with no computer control system on a mission must be
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MATHEMATICS A PRACT ODYSSEY -WEBASSIGN
- On average, 100 customers arrive per hour at Gotham City Bank. It takes a teller an average of two minutes to serve a customer. Interarrival and service times are exponentially distributed. The bank currently has four tellers working. The bank manager wants to compare the following two systems with regard to the average number of customers present in the bank and the probability that a customer will spend more than eight minutes in line. System 1: Each teller has his or her own line (and no moving between lines is permitted). Arriving customers are equally likely to choose any teller. System 2: All customers wait in a single line for the first available teller. Help the bank manager reach a decision by filling the following table. If needed, round your answers to one decimal digit. Average number of customers Prob (wait > 8') System 1 ________________________________________ % System 2 _________________________________________%arrow_forwardConsider a production system composed of two machines, where only one machine needs to be operational at any given time. The breakdown probability of any operational machine on any given day is 0.2. In case of a machine failure, the production is stopped for the day, and is resumed the next day with the other machine (if available). The repair job of the failed machine also starts the next day. It takes two days to repair a machine, and both machines can be repaired simultaneously.1) Define the state space and draw the state transition diagram.2) Starting with two available machines at the beginning of the first day, what is the probability that both machines are unavailable at the end of the 3rd day?3) In the long run, what is the ratio of the days that both machines are unavailable?arrow_forwardWhat is the solution of this question?arrow_forward
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- Assume the chances of failure of each component is given in Figure. What is the probability that the system works? .arrow_forwardIn a certain California city, projections for the next year are that there is a 20% chance that electronics jobs will increase by 200, a 50% chance that they will increase by 300, and a 30% chance they will decrease by 800. What is the expected change in the number of electronics jobs in that city in the next year?arrow_forwardThe weather in Columbus is either good, indifferent, or bad on any given day. If the weather is good today, there is a 40% chance it will be good tomorrow, a 40% chance it will be indifferent, and a 20% chance it will be bad. If the weather is indifferent today, there is a 60% chance it will be good tomorrow, and a 20% chance it will be indifferent. Finally, if the weather is bad today, there is a 10% chance it will be good tomorrow and a 30% chance it will be indifferent. a. What is the stochastic matrix, P, for this situation? b. Suppose there is a 40% chance of good weather today and a 60% chance of indifferent weather. What are the chances of bad weather tomorrow? c. Suppose the predicted weather for Monday is 90% indifferent weather and 10% bad weather. What are the chances for good weather on Wednesday? a. Create the stochastic matrix, P, where G is good, I is indifferent, and B is Bad. From: a P G B (Simplify your answers.) To: G I Barrow_forward
- Studies are often done by pharmaceutical companies to determine the effectiveness of a treatment program. Suppose that a new AIDS antibody drug is currently under study. It is given to patients once the AIDS symptoms have revealed themselves. Of interest is the average length of time in months patients live once starting the treatment. Two researchers each follow a different set of 40 AIDS patients from the start of treatment until their deaths. The following data (in months) are collected. Researcher 1: 3; 4; 11; 15; 16; 17; 22; 44; 37; 16; 14; 24; 25; 15; 26; 27; 33; 29; 35; 44; 13; 21; 22; 10; 12; 8; 40; 32; 26; 27; 31; 34; 29; 17; 8; 24; 18; 47; 33; 34 Researcher 2: 3; 14; 11; 5; 16; 17; 28; 41; 31; 18; 14; 14; 26; 25; 21; 22; 31; 2; 35; 44; 23; 21; 21; 16; 12; 18; 41; 22; 16; 25; 33; 34; 29; 13; 18; 24; 23; 42; 33; 29 Organize the data. Complete the tables below using the data provided. Researcher 1: Survival Length (in months) Frequency Relative Frequency…arrow_forwardThe weather in Columbus is either good, indifferent, or bad on any given day. If the weather is good today, there is a 40% chance it will be good tomorrow, a 30% chance it will be indifferent, and a 30% chance it will be bad. If the weather is indifferent today, there is a 50% chance it will be good tomorrow, and a 20% chance it will be indifferent. Finally, if the weather is bad today, there is a 10% chance it will be good tomorrow and a 30% chance it will be indifferent. a. What is the stochastic matrix, P, for this situation? b. Suppose there is a 10% chance of good weather today and a 90% chance of indifferent weather. What are the chances of bad weather tomorrow? c. Suppose the predicted weather for Monday is 40% indifferent weather and 60% bad weather. What are the chances for good weather on Wednesday? a. Create the stochastic matrix, P, where G is good, I is indifferent, and B is Bad. From: GIB a (Simplify your answers.) To: Garrow_forwardThe weather in Columbus is either good, indifferent, or bad on any given day. If the weather is good today, there is a 40% chance it will be good tomorrow, a 30% chance it will be indifferent, and a 30% chance it will be bad. If the weather is indifferent today, there is a 50% chance it will be good tomorrow, and a 20% chance it will be indifferent. Finally, if the weather is bad today, there is a 10% chance it will be good tomorrow and a 30% chance it will be indifferent. a. What is the stochastic matrix, P, for this situation? b. Suppose there is a 10% chance of good weather today and a 90% chance of indifferent weather. What are the chances of bad weather tomorrow? c. Suppose the predicted weather for Monday is 40% indifferent weather and 60% bad weather. What are the chances for good weather on Wednesday?arrow_forward
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