Question no 1

Question 1 The positions of wild flowers of a particular species in a meadow may be assumed to be reasonably modelled by a two-dimensional Poisson process with density A = 0.08 per square metre. A rectangular region 5 metres wide and 8 metres long is cordoned off. (a) Calculate the probability that the region does not contain any wild flowers of this species. (b) Calculate the probability that the region contains more than two wild flowers of this species. A wild flower of this species is selected at random in the meadow. (c) Write down the c.d.f. of the distance (in metres) from this flower to the nearest flower of this species. (d) Calculate the probability that the nearest flower of this species is more than 3 metres away. (e) Calculate the expected distance to the nearest flower of this species