TU Wien:Statistik und Wahrscheinlichkeitstheorie UE (Bura)/Übungen 2019W/4.3

Suppose cars arrive at a parking lot at a rate of 50 per hour. Assume that the process is modeled by a Poisson random variable with λ = 50.

(a) Compute the probability that in the next hour the number of cars that arrive at this parking lot will be between 54 and 62.

(b) Compare the value obtained in (a) with the probability calculated by using a Normal approximation.

Lösungsvorschlag[Bearbeiten | Quelltext bearbeiten]

(a)

> ppois(62, 50) - ppois(54, 50)
[1] 0.215303

The one above is wrong. We need to include 54 therefore we use either

> sum(dpois(54:62,50))
[1] 0.2616838

or

> ppois(62,50) - ppois(53,50)
[1] 0.2616838

or more correct would, but irrelevant for this example because there is not a lot of difference in this case

> ppois(62,50) - ppois(54,50) + dpois(54,50)
[1] 0.2616838

(b)

> pnorm(62.5,50,sqrt(50)) - pnorm(53.5,50,sqrt(50))
[1] 0.271759

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EDIT: 4.3