Applications of Probability & Two-dimensional Poisson Process Engineering Assignment Help

Assignment Task

Question

This question is intended to assess your understanding of the two-dimensional Poisson process and the ? 2 dispersion test. You should be able to answer this question after working through Part III of Book 2.
(a) 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 ? = 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). 
(iv) (1) Explain briefly (in one or two sentences) how you would simulate the positions of the palm trees in this region.
(2) Use the method that you have just described and groups of five digits from the 25th row of the table of random digits in the Handbook  to simulate the positions of the palm trees in the region. Calculate the coordinates of the palm trees to the nearest metre.
(3) Plot the positions of the palm trees on a sketch of the region.

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