Suppose that trees are distributed in a forest according to a two-dimensional Poisson process with parameter a, the expected number of trees per acre, equal to 80.
a. What is the probability that in a certain quarter-acre plot, there will be at most 16 trees?
b. If the forest covers 85,000 acres, what is the expected number of trees in the forest?
c. Suppose you select a point in the forest and construct a circle of radius .1 mile. Let X = the number of trees within that circular region. What is the pmf of X? [1 sq mile = 640 acres.]