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
7. 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 number of times your car is towed over the course of two months (60 days)?
Suppose that in addition to the city of Cambridge, your car may also be towed by MIT. On each day with probability 0.1, an MIT tow truck will pass by your ‘parking space,’ independently of all other days. If you car has not yet been towed by the city of Cambridge, the MIT tow truck will tow away your car. Assume that MIT operates independently of Cambridge’s meter maids.
(b) What is the probability distribution of the time (in days) till your car is towed a seventh time?
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