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Problem 4. Consider the following dynamics. If today is sunny, tomorrow will be sunny with a probability of 0.5, cloudy with a probability of 0.4 and rainy with a probability of 0.1. If today is cloudy, tomorrow will be sunny, cloudy, or rainy, with a probability of 0.5, 0.2, and 0.3, respectively. Lastly, if today is rainy, tomorrow will be sunny, cloudy, or rainy with a probability of 0.7, 0.2, and 0.1, respectively. a) Draw the corresponding Markov Chain. Clearly define your state space, draw the states and transitions, and include the probabilities on each arc. b) Starting on a Sunny day, what is the mean first passage time till a Rainy day. c) Starting on a rainy day, what is the mean recurrence time.

Problem 4. Consider the following dynamics. If today is sunny, tomorrow will be sunny with a probability of 0.5, cloudy with a probability of 0.4 and rainy with a probability of 0.1. If today is cloudy, tomorrow will be sunny, cloudy, or rainy, with a probability of 0.5, 0.2, and 0.3, respectively. Lastly, if today is rainy, tomorrow will be sunny, cloudy, or rainy with a probability of 0.7, 0.2, and 0.1, respectively. a) Draw the corresponding Markov Chain. Clearly define your state space, draw the states and transitions, and include the probabilities on each arc. b) Starting on a Sunny day, what is the mean first passage time till a Rainy day. c) Starting on a rainy day, what is the mean recurrence time.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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Problem 4. Consider the following dynamics. If today is sunny, tomorrow will be sunny with a probability of 0.5, cloudy with a probability of 0.4 and rainy with a probability of 0.1. If today is cloudy, tomorrow will be sunny, cloudy, or rainy, with a probability of 0.5, 0.2, and 0.3, respectively. Lastly, if today is rainy, tomorrow will be sunny, cloudy, or rainy with a probability of 0.7, 0.2, and 0.1, respectively. a) Draw the corresponding Markov Chain. Clearly define your state space, draw the states and transitions, and include the probabilities on each arc. b) Starting on a Sunny day, what is the mean first passage time till a Rainy day. c) Starting on a rainy day, what is the mean recurrence time.
Transcribed Image Text:Problem 4. Consider the following dynamics. If today is sunny, tomorrow will be sunny with a probability of 0.5, cloudy with a probability of 0.4 and rainy with a probability of 0.1. If today is cloudy, tomorrow will be sunny, cloudy, or rainy, with a probability of 0.5, 0.2, and 0.3, respectively. Lastly, if today is rainy, tomorrow will be sunny, cloudy, or rainy with a probability of 0.7, 0.2, and 0.1, respectively. a) Draw the corresponding Markov Chain. Clearly define your state space, draw the states and transitions, and include the probabilities on each arc. b) Starting on a Sunny day, what is the mean first passage time till a Rainy day. c) Starting on a rainy day, what is the mean recurrence time.
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