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Parking your car at MIT is expensive, so expensive that you decide that it must be cheaper to keep your car parked illegally in a tow zone and chance the occasional ticket or tow. On each day, a Cambridge meter maid will notice your illegally parked car with probability 0.25. Upon noticing your illegally parked car, with probability 0.8 he or she will only issue you a ticket; otherwise your car will be towed. All of this occurs independently on each day, and independent of what happens on other days.  (a) What is the expected time (in days) between successive times your car is towed?  (b) What is the standard deviation of the time (in days) between successive times your car is towed?

Parking your car at MIT is expensive, so expensive that you decide that it must be cheaper to keep your car parked illegally in a tow zone and chance the occasional ticket or tow. On each day, a Cambridge meter maid will notice your illegally parked car with probability 0.25. Upon noticing your illegally parked car, with probability 0.8 he or she will only issue you a ticket; otherwise your car will be towed. All of this occurs independently on each day, and independent of what happens on other days.  (a) What is the expected time (in days) between successive times your car is towed?  (b) What is the standard deviation of the time (in days) between successive times your car is towed?

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 16E: Consumer Preference In a population of 100,000 consumers, there are 20,000 users of Brand A, 30,000...
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Parking your car at MIT is expensive, so expensive that you decide that it must be cheaper to keep your car parked illegally in a tow zone and chance the occasional ticket or tow. On each day, a Cambridge meter maid will notice your illegally parked car with probability 0.25. Upon noticing your illegally parked car, with probability 0.8 he or she will only issue you a ticket; otherwise your car will be towed. All of this occurs independently on each day, and independent of what happens on other days. 

(a) What is the expected time (in days) between successive times your car is towed? 

(b) What is the standard deviation of the time (in days) between successive times your car is towed? 

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