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 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 10% chance of good weather today and a 90% chance of indifferent weather. What are the chances of bad weather tomorrow? c. Suppose the predicted weather for Monday is 40% indifferent weather and 60% bad weather. What are the chances for good weather on Wednesday?
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 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 10% chance of good weather today and a 90% chance of indifferent weather. What are the chances of bad weather tomorrow? c. Suppose the predicted weather for Monday is 40% indifferent weather and 60% bad weather. What are the chances for good weather on Wednesday?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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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 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 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 10% chance of good weather today and a 90% chance of indifferent weather. What are the
chances of bad weather tomorrow?
c. Suppose the predicted weather for Monday is 40% indifferent weather and 60% bad weather. What are the
chances for good weather on Wednesday?
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