Shakira's concerts behave like a Markov chain. If the current concert gets cancelled, then there is an 80% chance that the next concert will be cancelled also. However, if the current concert does not get cancelled, then there is only a 60% chance that the next concert will be cancelled. What is the long-run probability that a concert will be cancelled?

Shakira's concerts behave like a Markov chain. If the current concert gets cancelled, then there is an 80% chance that the next concert will be cancelled also. However, if the current concert does not get cancelled, then there is only a 60% chance that the next concert will be cancelled. What is the long-run probability that a concert will be cancelled?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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 Markov chain. If the ratings are high this week, they will be high, average, or low next week with probabilities 40%, 10%, and 50% respectively. If the ratings are average this week, they will be high, average, or low next week with probabilities 60%, 20%, and 20% respectively. If the ratings are low this week, they will be high, average, or low next week with probabilities 70%, 20%, and 10% respectively. Write all answers as 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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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.
Central topic markov chains: Every summer the Yates de los Lagos owners association decides if its annual regatta will be held in June, July or August. If it takes place in June, the probability of good weather is ¾; and if these conditions exist, the regatta of the next year it will be done in June with probability 2/3, in July with probability 1/6 or in August with probability 1/6; but if there is bad weather, next year's regatta will take place in July or August with equal probabilities. If the competition is held in July, good and bad weather have equal probabilities; if there is good weather, the next year's regatta will be held in July; If there is bad weather, the next regatta will take place in August with probability of 2/3 or in June with probability of 1/3. If the regatta takes place in August, the probability of good weather is 2/5; and if there are good conditions atmospheric conditions, next year's regatta will take place in July or August, with equal probabilities; but…
The purchase patterns for two brands of toothpaste can be expressed as a Markov process with the following transition probabilities. To From Special B MDA Special B 0.90 0.10 MDA 0.02 0.98 (a)Which brand appears to have the most loyal customers? Explain. MDA has the most loyal customers because ( ) %? stay with them and only ( ) %? switch to the other brand, as opposed to Special B where only ( )%? stay with them and ( )%? switch. (b) What are the projected market shares for the two brands? (Enter exact numbers as integers, fractions, or decimals.) Special B?1=? MDA?2=?
A bus containing 100 gamblers arrives in Las Vegas on a Monday morning. The gamblers play only poker or blackjack, and never change games during the day. The gamblers' daily choice of game can be modeled by a Markov chain: 95% of the gamblers playing poker today will play poker tomorrow, and 80% of the gamblers playing blackjack today will play blackjack tomorrow. (a) Write down the stochastic (Markov) matrix corresponding to this Markov chain. (b) If 60 gamblers play poker on Monday, how many gamblers play blackjack on Tuesday? (c) Find the unique steady-state vector for the Markov matrix in part (a).
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ne bets $1. 0.45, he wins the game and with probability 1 - p = 0.55, he loses the game. His goal is to increase his capital to $3, and as soon as he does, the game is over. The game is also over if his capital is reduced to zero. Construct an absorbing Markov chain and answer the following questions. • What is the expected duration of the game? • What is the probability that he goes broke?
Shakira's concerts behave like a Markov chain. If the current concert gets cancelled, then there is an 90% chance that the next concert will be cancelled also. However, if the current concert does not get cancelled, then there is only a 50% chance that the next concert will be cancelled. What is the long-run probability that a concert will not be cancelled? a. 1/4 b. 1/10 c. 1/6 d. 1/2 e. 5/6 f. None of the others are correct
Answer the following questions.
At Suburban Community College, 30% of all business majors switched to another major the next semester, while the remaining 70% continued as business majors. Of all non-business majors, 10% switched to a business major the following semester, while the rest did not. Set up these data as a Markov transition matrix. HINT [See Example 1.] (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.