3. Describe a Poisson distribution. Give two examples of a Poisson distribution. How are 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).