Solution Found!
Suppose that plants of a particular species are randomly
Chapter 4, Problem 173SE(choose chapter or problem)
Problem 173SE
Suppose that plants of a particular species are randomly dispersed over an area so that the number of plants in a given area follows a Poisson distribution with a mean density of λ plants per unit area. If a plant is randomly selected in this area, find the probability density function of the distance to the nearest neighboring plant. [Hint: If R denotes the distance to the nearest neighbor, then P( R > r ) is the same as the probability of seeing no plants in a circle of radius r .]
Questions & Answers
QUESTION:
Problem 173SE
Suppose that plants of a particular species are randomly dispersed over an area so that the number of plants in a given area follows a Poisson distribution with a mean density of λ plants per unit area. If a plant is randomly selected in this area, find the probability density function of the distance to the nearest neighboring plant. [Hint: If R denotes the distance to the nearest neighbor, then P( R > r ) is the same as the probability of seeing no plants in a circle of radius r .]
ANSWER:
Answer:
Step 1 of 1:
The number of plants in a given area follows a Poisson distribution with a mean density of plants per unit area.
If a plant is randomly selected in this area, find the probability density function of the distance to the nearest neighbouring plant.
Since the number of plants in a given area follows a Poisson distribution with a mean density of plants per unit area.
Hence the number of plants in an area of units has a Poisson distribution.
Then the mean density of Poisson distribution for given area will become,
Let denote the number of plants in a region with surface area