2. At a certain location in downtown Chicago, there are ample parking spaces on the street.

At that location, cars are parked illegally and independently of the police inspection times according to a Poisson process with rate λ. The duration of the time a car is illegally parked is exponentially distributed with mean 10 minutes. Starting at midnight, Chicago police inspect that location 24 hours a day, every 30 minutes, and fine the cars that are parked illegally since the last inspection. Determine the percentage of cars that are parked illegally and are caught.

Hint: Between 0 and 30, let Y be the time a random car is illegally parked on the street. Suppose that the car parked illegally at Y is left parked for X units of time. Let A be the event that it is caught. Show that 100 ·

is the desired percentage and calculate it.

Transcribed Image Text:

30 1 P(A Y y)dy 30