One model for plant competition assumes that there is a zone of resource depletion

Chapter 3, Problem 3.198

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One model for plant competition assumes that there is a zone of resource depletion around each plant seedling. Depending on the size of the zones and the density of the plants, the zones of resource depletion may overlap with those of other seedlings in the vicinity. When the seeds are randomly dispersed over a wide area, the number of neighbors that any seedling has within an area of size A usually follows a Poisson distribution with mean equal to A d, where d is the density of seedlings per unit area. Suppose that the density of seedlings is four per square meter. What is the probability that a specified seeding has a no neighbors within 1 meter? b at most three neighbors within 2 meters?

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