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Math · Statistics And Probability
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STOCHASTIC PROCESS

The Poisson process

3 points The number of cars arriving to the university parking every morning follows a non- is Poisson process with a constant average of 100 cars per hour between 8 and 8:30 that increases linearly to 250 between 8:30 and 8:45 and continues to increase to 350 between 8:45 and 9 to then decrease to 100 per hour between 9 and 9:30. The parking has 150 spots and opens every morning at 8 a.m. with no car inside. a) [0.75 points] Find the expectation of the number of cars that get to the university parking by time t. b) 0.5 points Assuming that no car leaves before 9:30, use R (without simulation) to find the time you should get to the parking in order to find a free spot at least the 80% of the days.

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