A certain television show airs weekly. Each time it airs, its ratings are categorized as "high,""average," or "low," and transitions between these categorizations each week behave like a Markovchain. If the ratings are high this week, they will be high, average, or low next week with probabilities40%, 10%, and 50% respectively. If the ratings are average this week, they will be high, average, or lownext week with probabilities 60%, 20%, and 20% respectively. If the ratings are low this week, they willbe high, average, or low next week with probabilities 70%, 20%, and 10% respectively. Write all answersas integers or decimals.If the ratings are average this week, what is the probability that they will be low two weeks from now?If the ratings are average the first week, what is the probability that they will be low the second week?If the ratings are low the first week, what is the probability that they will be high the third week?

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Answered: A certain television show airs weekly.…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.5: Markov Chain

Problem 47E: Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.

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Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.
A food manufacturer has to decide how many batches of a product to produce next week. If one batch is produced, the profit will be $15,000. If two batches are produced, but the demand is only sufficient for one batch, then a loss of $5,000 will occur. If two batches are produced and the demand is equal to two batches, then a profit of $20,000 will occur. The food manufacturer estimates the probabilities of these two outcomes as being 0.4 and 0.6 respectively. A separate forecasting tool, estimates demand will equal two batches. In the past, this tool has correctly predicted demand in 60% of weeks, irrespective of what the level of demand turned out to be. To maximise his expected profit, the manufacturer should: Select one: a. produce 1 batch b. produce 2 batches c. be indifferent between producing 1 or 2 batches d. seek more information, as it is not possible to compute the expected profits from this information
A system consists of five components, each can be operational or not. Each day one operational component is used and it will fail with probability 20%. Any time there no operational components at the end of a day, maintenance will be performed and all non-operational components will be repaired (with probability 1). The system does not perform any other tasks on the day of repairs. Model the system as a Markov chain Write down equations for determining long-run proportions. Suppose that you are interested in the average number of days that the system is under repair. Explain how you would find it using your model.
There is a 30% chance that any current client of company A will switch to company B this year. There is a 20% chance that any client of company B will switch to company A this year. If these probabilities are stable over the years, and if company A has 1000 clients and company B has 1000 clients, how many clients will each company have in each of the next two years?
answer using markov systems.
A system contains two components, A and B. The system will function only if both components function. The probability that A functions is 0.98, the probability that B functions is 0.95, and the probability that either A or B functions is 0.99. What is the probability that the system functions?
In an amusement arcade there is a horse race with horses coloured red, yellow and green. Only one player can play this game at any time and the outcomes of each race are independent of previous races. You can either bet 10p or 20p. If you bet 10p then each horse is equally likely to win. If you bet 20p the corresponding probabilities are 50%, 30% and 20%, respectively. Three times as many people bet 10p as do 20p. Given red wins, what is the probability it had been a 20p bet? 0.333 0.300 0.313 0.298
A certain stock price has been observed to follow a pattern. If the stock price goes up one day, there's a 20% chance of it rising tomorrow, a 30% chance of it falling, and a 50% chance of it remaining the same. If the stock price falls one day, there's a 35% chance of it rising tomorrow, a 50% chance of it falling, and a 15% chance of it remaining the same. Finally, if the price is stable on one day, then it has a 50-50 change of rising or falling the next day. Find transition probability matrix for this Markov chain, if we list states in the order: (rising, falling, constant)
In an amusement arcade there is a horse race with horses coloured red, yellow and green. Only one player can play this game at any time and the outcomes of each race are independent of previous races. You can either bet 10p or 20p. If you bet 10p then each horse is equally likely to win. If you bet 20p the corresponding probabilities are 50% (red), 30% (yellow) and 20% (green). Three times as many people bet 10p as do 20p. What is the probability a red horse wins? 0.375 0.267 0.367 0.308
A system has five components connected as shown in the diagram. Assume A, B, C, D, and E function independently. If the probabilities that A, B, C, D, and E fail 0.05, 0.04, 0.10, 0.04, and 0.06 respectively, what is the probability that the system functions?
Topic: MARKOV CHAINS In a sample of 400 Internet subscribers taken in late 2000, 80% were connected by telephone, and the rest via cable modem.the rest via cable modem. At the end of 2001, the number of subscribers who switched from telephone to cable modem connection was 110; and the number of subscribers who switched from telephone to cable modem connection was 110.modem connection was 110; and the number of subscribers switching from cable modem to telephone connection was 24. B) What proportion of subscribers will each system have by the end of 2002?
Baseball's World Series is a maximum of seven games, with the winner being the first team to win four games. Assume that the Atlanta Braves are playing the Minnesota Twins in the World Series and that the first two games are to be played in Atlanta, the next three games at the Twins' ballpark, and the last two games, if necessary, back in Atlanta. Taking into account the projected starting pitchers for each game and the home field advantage, the probabilities of Atlanta winning each game are as follows: Game 1 2 3 4 5 6 7 Probability of Win 0.45 0.42 0.46 0.5 0.46 0.41 0.52 Set up a spreadsheet simulation model in whether Atlanta wins each game is a random variable. What is the probability that the Atlanta Braves win the World Series? If required, round your answer to two decimal places.fill in the blank 1 What is the average number of games played regardless of winner? If required, round your answer to one decimal place.

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