A PWR plant has two residual heat removal (RHR) pumps, with pump 1 operating and pump 2 in standby whenever the RHR system is activated. Both pumps have a MTTF of 1/2 and the service crew can repair a pump during a mean time interval of 1/μ. The failure probability of the pumps in standby is negligibly small. (a) Define three states of the RHR pump system and set up a Markov chain model for the probabilities P (t), n = 1,2,3.
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- Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.Consider two machines that are maintained by a single repairman. Each machine functions for an exponentially distributed amount of time with rate λ=2 before it fails. The repair times for each unit are exponential with rate μ=1.The Markov chain model for this situation has state space indicating the number of machines that are in the repair shop: S={0,1,2}. Notice that you move from 0 to 1 if one of the two machines breaks down. You move from 1 to 0 when the machine in the repair room is repaired.What are the difficulties in estimating the following model? Use as much detail as possible in answering this question while considering the Gauss-Markov assumptions and OLS estimator. Economic productivity = β0 + β1Unemployment + β2Innovation + θiControls + ei Where unemployment is the average unemployment rate of a country and innovation is an index of R&D performance.
- Suppose a math professor collects data on the probability that students attending a given class meeting will attend the next one. He finds that 95% of students who attended a given class meeting will attend the following class meeting and that 25% of students who do not attend attend a given class meeting will not attend the next one. Build a discrete dynamical system model using linear algebra. Be sure to state your transition matrix explicitly. What percentage of students does your model predict will be attending class meetings by the end of the semester (in the long run)?If OLS estimators satisfy asymptotic normality, it implies that: Select one: O a. they are approximately normally distributed in large enough sample sizes they are approximately normally distributed in samples of less than 10 observations. O c. they have a constant mean equal to zero and a variance equal to o?. O d. they have a constant mean equal to one and a variance equal to a.In airline applications, failure of a component can result in catastrophe. As a result, many airline components utilize something called triple modular redundancy. This means that a critical component has two backup components that may be utilized should the initial component fail. Suppose a certain critical airline component has a probability of failure of 0.0065 and the system that utilizes the component is part of a triple modular redundancy. (a) Assuming each component's failure/success is independent of the others, what is the probability all three components fail, resulting in disaster for the flight? (b) What is the probability at least one of the components does not fail? (a) The probability is (Round to eight decimal places as needed.)
- Consider the two state switch model from the videos with state space S = {1,2} and transition rate matrix where A = 1 and u = 1.5. (a) If the system is in state 1, what is the mean time until it transitions to state 2? Number (b) Evaluate P11 (0) Number (C) Evaluate P11 (0.4) Number (d) Evaluate P21 (0.4) NumberConsider two machines that are maintained by a single repairman. Each machine functions for an exponentially distributed amount of time with rate λ before it fails. The repair times for each unit are exponential with rate μ. Formulate a Markov chain model for this situation with state space indicating the number of machines that are in the repair shop: S={0,1,2}. Notice that you move from 0 to 1 if one of the two machines breaks down. You move from 1 to 0 when the machine in the repair room is repaired. 2. Same as above but now machines are repaired in the order in which they fail. Each machine functions for an exponentially distributed amount of time with rate λi before it fails. The repair times for each unit are exponential with rate μi. The state space has nodes that are keep track of the machine that is at the repair shop (in case there is only one) and keeps track of which machine is worked on in case there are two machines at the repair shop. That is the state space is S={0,…A major long-distance telephone company (company A) has studied the tendency of telephone users to switch from one carrier to another. The company believes that over successive six-month periods, the probability that a customer who uses A's service will switch to a competing service is 0.2 and the probability that a customer of any competing service will switch to A is 0.3. (a) Find a transition matrix for this situation. (b) If A presently controls 60% of the market, what percentage can it expect to control six months from now? (c) What percentage of the market can A expect to control in the long run? (a) Find a transition matrix for this situation. Let "Comp" stand for "a competing service." A Comp A Comp (Type integers or decimals.) (b) If A presently controls 60% of the market, what percentage can it expect to control six months from now? Company A can expect to control % of the market six months from now. (c) What percentage of the market can A expect to control in the long run?…
- In airline applications, failure of a component can result in catastrophe. As a result, many airline components utilize something called triple modular redundancy. This means that a critical component has two backup components that may be utilized should the initial component fail. Suppose a certain critical airline component has a probability of failure of 0.0052 and the system that utilizes the component is part of a triple modular redundancy. (a) Assuming each component's failure/success is independent of the others, what is the probability all three components fail, resulting in disaster for the flight? (b) What the probability least one of the components does not fail? (a) The probability is. (Round to eight decimal places as needed.) (b) The probability is (Round to eight decimal places as needed.) O C Next 2:39If she made the last free throw, then her probability of making the next one is 0.7. On the other hand, If she missed the last free throw, then her probability of making the next one is 0.2. Assume that state 1 is Makes the Free Throw and that state 2 is Misses the Free Throw. (1) Find the transition matrix for this Markov process. P =Suppose that the model pctstck = Bo + Bfunds + Bzrisktol + u satisfies the first four Gauss-Markov assumptions, where pctstck is the percentage of a worker's pension invested in the stock market, funds is the number of mutual funds that the worker can choose from, and risktol is some measure of risk tolerance (larger risktol means the person has a higher tolerance for risk). If funds and risktol are positively correlated, what is the inconsistency in Bj, the slope coefficient in the simple regression of pctstck on funds?