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 40% chance it will be indifferent, and a 20% chance it will be bad. If the weather is indifferent today, there is a 60% chance it will be good tomorrow, and a 20% chance it will be indifferent. Finally, if the weather is bad today, there is a 10% chance it will be good tomorrow and a 30% chance it will be indifferent. a. What is the stochastic matrix, P, for this situation? b. Suppose there is a 40% chance of good weather today and a 60% chance of indifferent weather. What are the chances of bad weather tomorrow? c. Suppose the predicted weather for Monday is 90% indifferent weather and 10% bad weather. What are the chances for good weather on Wednesday?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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 40% chance it will be indifferent, and a 20% chance it will be bad. If the weather is indifferent today, there is a 60%
chance it will be good tomorrow, and a 20% chance it will be indifferent. Finally, if the weather is bad today, there is a 10% chance it will be
good tomorrow and a 30% chance it will be indifferent.
a. What is the stochastic matrix, P, for this situation?
b. Suppose there is a 40% chance of good weather today and a 60% chance of indifferent weather. What are the chances of bad
weather tomorrow?
c. Suppose the predicted weather for Monday is 90% indifferent weather and 10% bad weather. What are the chances for good weather
on Wednesday?
a. Create the stochastic matrix, P, where G is good, I is indifferent, and B is Bad.
From:
a
P
G
B
(Simplify your answers.)
To:
G
I
B
Transcribed Image Text: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 40% chance it will be indifferent, and a 20% chance it will be bad. If the weather is indifferent today, there is a 60% chance it will be good tomorrow, and a 20% chance it will be indifferent. Finally, if the weather is bad today, there is a 10% chance it will be good tomorrow and a 30% chance it will be indifferent. a. What is the stochastic matrix, P, for this situation? b. Suppose there is a 40% chance of good weather today and a 60% chance of indifferent weather. What are the chances of bad weather tomorrow? c. Suppose the predicted weather for Monday is 90% indifferent weather and 10% bad weather. What are the chances for good weather on Wednesday? a. Create the stochastic matrix, P, where G is good, I is indifferent, and B is Bad. From: a P G B (Simplify your answers.) To: G I B
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