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Problem 3. A study of male criminals in Philadelphia found that the probability that one type of offense is followed by another type can be described by the following transition table: Current Nonindex Injury Theft Damage Combination Next Nonindex Injury Theft Damage Combination 0.645 0.099 0.152 0.033 0.071 0.611 0.090 0.514 0.118 0.609 0.042 0.523 0.179 0.138 0.128 0.033 0.067 0.271 0.030 0.107 0.178 0.064 0.093 0.183 0.022 (a) For a criminal who commits theft, what is the probability that his next crime is also a theft? (b) For a criminal who commits theft, what is the probability that his second crime after that is also a theft? (c) If this trends continue, what are the long-term probabilities for each type of crime?

Problem 3. A study of male criminals in Philadelphia found that the probability that one type of offense is followed by another type can be described by the following transition table: Current Nonindex Injury Theft Damage Combination Next Nonindex Injury Theft Damage Combination 0.645 0.099 0.152 0.033 0.071 0.611 0.090 0.514 0.118 0.609 0.042 0.523 0.179 0.138 0.128 0.033 0.067 0.271 0.030 0.107 0.178 0.064 0.093 0.183 0.022 (a) For a criminal who commits theft, what is the probability that his next crime is also a theft? (b) For a criminal who commits theft, what is the probability that his second crime after that is also a theft? (c) If this trends continue, what are the long-term probabilities for each type of crime?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 3. A study of male criminals in Philadelphia found that the probability that one type of offense is followed by another type can be described by the following transition table: Current Nonindex Injury Theft Damage Combination Next Nonindex Injury Theft Damage 0.645 0.099 0.152 0.033 0.611 0.514 0.609 0.523 0.138 0.128 0.033 0.067 0.271 0.030 0.107 0.178 0.093 0.183 0.064 0.022 Combination 0.071 0.090 0.118 0.042 0.179 (a) For a criminal who commits theft, what is the probability that his next crime is also a theft? (b) For a criminal who commits theft, what is the probability that his second crime after that is also a theft? (c) If this trends continue, what are the long-term probabilities for each type of crime?
Transcribed Image Text:Problem 3. A study of male criminals in Philadelphia found that the probability that one type of offense is followed by another type can be described by the following transition table: Current Nonindex Injury Theft Damage Combination Next Nonindex Injury Theft Damage 0.645 0.099 0.152 0.033 0.611 0.514 0.609 0.523 0.138 0.128 0.033 0.067 0.271 0.030 0.107 0.178 0.093 0.183 0.064 0.022 Combination 0.071 0.090 0.118 0.042 0.179 (a) For a criminal who commits theft, what is the probability that his next crime is also a theft? (b) For a criminal who commits theft, what is the probability that his second crime after that is also a theft? (c) If this trends continue, what are the long-term probabilities for each type of crime?
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