15. Plant Density One model for plant competition assumes that there is a zone of resource depletion around each plant seedling. When the seeds are randomly dispersed over a wide area, the number of neighbors that a seedling may have usually follows a Poisson distribution with a mean equal to the density of seedlings per unit area. Suppose that the density of seedlings is four per square meter (m2 ).

a. What is the probability that a given seedling has no neighbors within 1m2?

b. What is the probability that a seedling has at most three neighbors per m2?

c. What is the probability that a seedling has five or more neighbors per m2?

d. Use the fact that the mean and variance of a Poisson random variable are equal to find the proportion of neighbors that would fall into the interval m 62s .

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