The positions of trees in a forest may be assumed to be reasonably modelled by a two-dimensional Poisson process with density A = 0.01 per square metre. (a) Calculate the expected distance (in centimetres) from a randomly selected point in the forest to the nearest tree. (b) A rectangular region of the forest 10 metres long and 15 metres wide is cordoned off. (i) Calculate the probability that the region contains one tree. (ii) Calculate the probability that the region contains at least three trees. (iii) Use the number a = 0.4082, which is a random observation from the uniform distribution (0, 1), to simulate the number of trees in the region