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Linear Algebra and Its Applications | 5th Edition | ISBN: 9780321982384 | Authors: David C. Lay; Steven R. Lay; Judi J. McDonald
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Refer to Exercise 4. In the long run, how likely is it for

Chapter 4, Problem 14E

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QUESTION:

Problem 14E

Refer to Exercise 4. In the long run, how likely is it for the weather in Columbus to be good on a given day?

Reference:

The weather in Columbus is either good, indifferent, or bad on any given day. If the weather is good today, there is a 40% chance it will be good tomorrow, a 30% chance it will be indifferent, and a 30% chance it will be bad. If the weather is indifferent today, there is a 50% chance it will be good tomorrow, and a 20% chance it will be indifferent. Finally, if the weather is bad today, there is a 30% chance it will be good tomorrow and a 40% chance it will be indifferent.

a. What is the stochastic matrix for this situation?

b. Suppose there is a 50% chance of good weather today and a 50% chance of indifferent weather. What are the chances of bad weather tomorrow?

c. Suppose the predicted weather for Monday is 60% indifferent weather and 40% bad weather. What are the chances for good weather on Wednesday?

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QUESTION:

Problem 14E

Refer to Exercise 4. In the long run, how likely is it for the weather in Columbus to be good on a given day?

Reference:

The weather in Columbus is either good, indifferent, or bad on any given day. If the weather is good today, there is a 40% chance it will be good tomorrow, a 30% chance it will be indifferent, and a 30% chance it will be bad. If the weather is indifferent today, there is a 50% chance it will be good tomorrow, and a 20% chance it will be indifferent. Finally, if the weather is bad today, there is a 30% chance it will be good tomorrow and a 40% chance it will be indifferent.

a. What is the stochastic matrix for this situation?

b. Suppose there is a 50% chance of good weather today and a 50% chance of indifferent weather. What are the chances of bad weather tomorrow?

c. Suppose the predicted weather for Monday is 60% indifferent weather and 40% bad weather. What are the chances for good weather on Wednesday?

ANSWER:

Solution 14E

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