Question

Suppose that trees are distributed in a forest according to a two-dimensional Poisson process with parameter α, the expected number of trees per acre, equal to 40.

(a) What is the probability that in a certain quarter-acre plot, there will be at most 13 trees? (Round your answer to three decimal places.)

(b) If the forest covers 65,000 acres, what is the expected number of trees in the forest?

_________trees

(c) Suppose you select a point in the forest and construct a circle of radius 0.1 mile. Let X = the number of trees within that circular region. What is the pmf of X? [Hint: 1 sq mile = 640 acres.]

p(x) = _______

Answer 1