3. Describe a Poisson distribution. Give two examples of a Poisson distribution. How is the expected value and standard deviation determined?  a.Suppose there are trees distributed in a forest according to a process of Poisson in two dimensions, with parameter α and that the expected number of trees per acre equals 80. i. What is the probability that in a certain quarter acre lot there are at most 16 trees? ii. If the forest covers 85,000 acres, what is the expected number of trees in the forest? iii. Suppose a point in the forest is selected and a circle of .1 mile radius. Let X be the number of trees within that circular region, what is the distribution function of X? (a square mile equals 640 acres).

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