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Sally and Mike are playing frisbee at the beach. When Sally throws the frisbee the probability is 0.13 that it comes back to Sally, the probability is 0.7 that it goes to Mike, and the probability is 0.17 that the dog runs away with the frisbee. When Mike throws the frisbee there is a 0.62 probability that Sally gets it, a 0.27 probability that it comes back to Mike, and a 0.11 probability that the dog runs away with the frisbee. Treat this as a 3--state Markov Chain with the dog being an absorbing state. (a) If Mike has the frisbee, what is the expected value for the number of times the frisbee will be thrown before the dog gets the frisbee and runs away with it? (Give your answer correct to 2 decimal places.) times thrown (b) If Mike has the frisbee, what is the expected value for the number of times Mike will throw the frisbee before the dog gets it? (Give your answer correct to 2 decimal places.) times Mike throws

Sally and Mike are playing frisbee at the beach. When Sally throws the frisbee the probability is 0.13 that it comes back to Sally, the probability is 0.7 that it goes to Mike, and the probability is 0.17 that the dog runs away with the frisbee. When Mike throws the frisbee there is a 0.62 probability that Sally gets it, a 0.27 probability that it comes back to Mike, and a 0.11 probability that the dog runs away with the frisbee. Treat this as a 3--state Markov Chain with the dog being an absorbing state. (a) If Mike has the frisbee, what is the expected value for the number of times the frisbee will be thrown before the dog gets the frisbee and runs away with it? (Give your answer correct to 2 decimal places.) times thrown (b) If Mike has the frisbee, what is the expected value for the number of times Mike will throw the frisbee before the dog gets it? (Give your answer correct to 2 decimal places.) times Mike throws

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.5: Markov Chain
Problem 15E: Smokers and Non smokers In a population of 10,000, there are 5000 non-smokers, 2500 smokers of one...
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Sally and Mike are playing frisbee at the beach. When Sally throws the frisbee the probability is 0.13 that it comes back to Sally, the probability is 0.7 that it goes to Mike, and the probability is 0.17 that the dog runs away with the frisbee. When Mike throws the frisbee there is a 0.62 probability that Sally gets it, a 0.27 probability that it comes back to Mike, and a 0.11 probability that the dog runs away with the frisbee. Treat this as a 3--state Markov Chain with the dog being an absorbing state. (a) If Mike has the frisbee, what is the expected value for the number of times the frisbee will be thrown before the dog gets the frisbee and runs away with it? (Give your answer correct to 2 decimal places.) times thrown (b) If Mike has the frisbee, what is the expected value for the number of times Mike will throw the frisbee before the dog gets it? (Give your answer correct to 2 decimal places.) times Mike throws
Transcribed Image Text:Sally and Mike are playing frisbee at the beach. When Sally throws the frisbee the probability is 0.13 that it comes back to Sally, the probability is 0.7 that it goes to Mike, and the probability is 0.17 that the dog runs away with the frisbee. When Mike throws the frisbee there is a 0.62 probability that Sally gets it, a 0.27 probability that it comes back to Mike, and a 0.11 probability that the dog runs away with the frisbee. Treat this as a 3--state Markov Chain with the dog being an absorbing state. (a) If Mike has the frisbee, what is the expected value for the number of times the frisbee will be thrown before the dog gets the frisbee and runs away with it? (Give your answer correct to 2 decimal places.) times thrown (b) If Mike has the frisbee, what is the expected value for the number of times Mike will throw the frisbee before the dog gets it? (Give your answer correct to 2 decimal places.) times Mike throws
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