Task 4 The incidence of rust attack along a gas pipeline can be modeled as a Poisson process with intensity λ per kilometer. This means that the number of rust attacks per kilometer along the pipeline can assumed to be Poisson distributed with expected value λ. Assume initially that it is known that λ = 5. The distance between two subsequent rust attacks is exponentially distributed with parameter λ (the distance between subsequent events in a Poisson process is exponentially distributed), and we still assume that λ = 5 per kilometer. b) What is the expected distance between two successive rust attacks? What is the probability that the distance between two consecutive rust attacks is more than 200 meters? What is the probability that the distance between two successive rust attacks is less than 300 meters? What is the probability that the distance between two consecutive rust attacks is between 200 and 300 meters?
Task 4
The incidence of rust attack along a gas pipeline can be modeled as a Poisson process with
intensity λ per kilometer. This means that the number of rust attacks per kilometer along the pipeline can
assumed to be Poisson distributed with expected value λ.
Assume initially that it is known that λ = 5.
The distance between two subsequent rust attacks is exponentially distributed with parameter λ (the distance
between subsequent events in a Poisson process is exponentially distributed), and we still assume
that λ = 5 per kilometer.
b) What is the expected distance between two successive rust attacks?
What is the probability that the distance between two consecutive rust attacks is more than 200
meters?
What is the probability that the distance between two successive rust attacks is less than
300 meters?
What is the probability that the distance between two consecutive rust attacks is between 200
and 300 meters?
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