Using the following: Solve: two-dimensional Poisson process and the x² dispersion test. The positions of palm trees on a large island may be assumed to be randomly located according to a two-dimensional Poisson process with density λ = 20 per square kilometre. A rectangular region of the island that is 300 metres long by 400 metres wide is marked out for detailed study. (i) Write down the probability distribution of N, the number of palm trees in this region. (ii) Calculate the probability that the region contains more than three palm trees. (iii) Simulate the number of palm trees in this region using the number u = 0.5218, which is a random observation from the uniform distribution (0.1).
Using the following: Solve: two-dimensional Poisson process and the x² dispersion test. The positions of palm trees on a large island may be assumed to be randomly located according to a two-dimensional Poisson process with density λ = 20 per square kilometre. A rectangular region of the island that is 300 metres long by 400 metres wide is marked out for detailed study. (i) Write down the probability distribution of N, the number of palm trees in this region. (ii) Calculate the probability that the region contains more than three palm trees. (iii) Simulate the number of palm trees in this region using the number u = 0.5218, which is a random observation from the uniform distribution (0.1).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Using the following:
Solve:
two-dimensional Poisson process and the x² dispersion test.
The positions of palm trees on a large island may be assumed to be
randomly located according to a two-dimensional Poisson process with
density A = 20 per square kilometre. A rectangular region of the island
that is 300 metres long by 400 metres wide is marked out for detailed
study.
(i) Write down the probability distribution of N, the number of palm
trees in this region.
(ii) Calculate the probability that the region contains more than three
palm trees.
(iii) Simulate the number of palm trees in this region using the number
u = 0.5218, which is a random observation from the uniform
distribution U (0, 1).
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