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 reg

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter3: Matrices
Section3.7: Applications
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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 if you have bad weather, the next regatta will be held in June with probability 1/3 or in July with probability 2/3. In what proportion of the time is the regatta held in June, July or August respectively?

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