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?
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- 12. Robots have been programmed to traverse the maze shown in Figure 3.28 and at each junction randomly choose which way to go. Figure 3.28 (a) Construct the transition matrix for the Markov chain that models this situation. (b) Suppose we start with 15 robots at each junction. Find the steady state distribution of robots. (Assume that it takes each robot the same amount of time to travel between two adjacent junctions.)Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.A manufacturer has a machine that if it ran all day today has a proba- bility of 0.2 of breaking down sometime during the day tomorrow. When the machine breaks down, it goes offline for the remainder of the day and then a technician will spend the next day (after the breakdown) repairing it. A newly repaired machine only has a proability of 0.1 of breaking down sometime tomorrow. (a) Formulate the evolution of the status of the machine at the end of the day as a Markov Chain by identifying the three possible states at the end of the day and providing the transition probabilities between these states. (b) Determine the expected first passage times, µij , for all combinations of states i and j where i cannot equal to j (i.e., you don’t need to determine the recurrence times). You must provide the set of equations used to calculate these µij (micro with lowercase i and j). (c) Using your results from (b): (i) Identify the expected number of full days that the machine will remain…
- According the Ghana Statistical Service data collected in 2020 shows that, 5% of individuals living within the city move to the rural areas during a one-year period, while 4% of individuals living in the rural areas move to the city a one-year period. Assuming that, this process is modeled by a Markov process with two states: city and rural areasa) i. Prepare the matrix of transition probabilitiesii. Compute the steady-state probabilities.iii. In a particular District, 40% of the population lives in the city, and 60% of the population lives in the suburbs. What population changes do your steady-state probabilities project for this metropolitan area?A coffee shop has two coffee machines, and only one coffee machine is in operation at any given time. A coffee machine may break down on any given day with probability 0.2 and it is impossible that both coffee machines break down on the same day. There is a repair store close to this coffee shop and it takes 2 days to fix the coffee machine completely. This repair store can only handle one broken coffee machine at a time. Define your own Markov chain and use it to compute the proportion of time in the long run that there is no coffee machine in operation in the coffee shop at the end of the day.Data collected from selected major metropolitan areas in the eastern United States show that 3% of individuals living within the city limits move to the suburbs during a one-year period, while 1% of individuals living in the suburbs move to the city during a one-year period. Answer the following questions assuming that this process is modeled by a Markov process with two states: city and suburbs. (a) Prepare the matrix of transition probabilities. To From City Suburbs City Suburbs (b) Compute the steady-state probabilities. (Enter your probabilities as fractions.) City?1= Suburbs?2=
- At Suburban Community College, 40% of all business majors switched to another major the next semester, while the remaining 60% continued as business majors. Of all non-business majors, 20% switched to a business major the following semester, while the rest did not. Set up these data as a Markov transition matrix. (Let 1 = business majors, and 2 = non-business majors.) calculate the probability that a business major will no longer be a business major in two semesters' time.The computer center at Rockbottom University has been experiencing computer downtime. Let us assume that the trials of an associated Markov process are defined as one-hour periods and that the probability of the system being in a running state or a down state is based on the state of the system in the previous period. Historical data show the following transition probabilities. To From Running Down Running 0.80 0.20 Down 0.30 0.70 (a) If the system is initially running, what is the probability of the system being down in the next hour of operation? (b) What are the steady-state probabilities of the system being in the running state and in the down state? (Enter your probabilities as fractions.) Running?1=Down?2=What are the Guass-Markov assumptions? What problems would happen if a gression model does not meet each of the assumptions? Briefly explain.
- Consider the problem of sending a binary message, 0 or 1, through a signal channelconsisting of several stages, where transmission through each stage is subject to a fixedprobability of error α. Suppose that X0 = 0 is the signal that is sent and let Xn, be thesignal that is received at the nth stage. Assume that {Xn} is a Markov chain with transitionprobabilities, Poo = P11 = 1- α and P01 = P10 = α, where 0 < α < 1.(a) Determine P {Xo = 0, X1 = 0, X2 = 0}, the probability that no error α occurs up tostage n = 2.(b) Determine the probability that a correct signal is received at stage 2.Please answer using markov chain with BTI upgradation onlyA cellphone provider classifies its customers as low users (less than 400 minutes per month) or high users (400 or more minutes per month). Studies have shown that 40% of people who were low users one month will be low users the next month and that 30% of the people who were high users one month will high users next month. a. Set up a 2x2 stochastic matrix with columns and rows labeled L and H that displays these transitions b. After many months, how many % of the customers are high users