Question
. A police car is on patrol in a neighborhood known for its gang activities. During a patrol, there is a 60% chance that the
. A police car is on patrol in a neighborhood known for its gang activities. During a patrol, there is a 60% chance that the location where the help is needed can be responded to in time, else the car will continue regular patrol. Upon receiving a call, there is a 10% chance for cancellation (in which case the car resumes its normal patrol) and a 30% chance that the car is already responding to a previous call. Otherwise the car arrives at the call scene. When the police arrives at the scene, there is a 10% chance that the instigators will have fled (in which case the car returns back to patrol) and a 40% chance that apprehension is made immediately. Else, the officers will search the area. If apprehension occurs, there is a 60% chance of transporting the suspects to the police station, else they are released, and the car returns to patrol. a) Express the probabilistic activities of the police patrol in the form of a transition matrix where the states are police on patrol, police responding to a call, police at call scene, police making an apprehension, and police transport suspects to police station. b) If the police car is currently at a call scene, determine the probability that an apprehension will take place in two patrols. c) Classify the states of the Markov chain.
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