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? (c) What is the expected number of times your car is towed over the course of two months (60 days)?

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? (c) What is the expected number of times your car is towed over the course of two months (60 days)?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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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