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Two-dimensional Poisson process. The number of plants of a
Chapter 4, Problem 12E(choose chapter or problem)
Two-dimensional Poisson process. The number of plants of a certain species in a certain forest has a Poisson distribution with mean 10 plants per acre. The number of plants in \(T\) acres therefore has a Poisson distribution with mean 10T .
a. What is the probability that there will be exactly 18 plants in a two-acre region?
b. What is the probability that there will be exactly 12 plants in a circle with radius 100 ft? (1 acre = \(43,560\mathrm{\ ft}^2\).)
c. The number of plants of a different type follows a Poisson distribution with mean \(\lambda\) plants per acre, where \(\lambda\) is unknown. A total of 5 plants are counted in a 0.1 acre area. Estimate \(\lambda\), and find the uncertainty in the estimate.
Equation Transcription:
Text Transcription:
T
43,560 ft^2
lambda
Questions & Answers
QUESTION:
Two-dimensional Poisson process. The number of plants of a certain species in a certain forest has a Poisson distribution with mean 10 plants per acre. The number of plants in \(T\) acres therefore has a Poisson distribution with mean 10T .
a. What is the probability that there will be exactly 18 plants in a two-acre region?
b. What is the probability that there will be exactly 12 plants in a circle with radius 100 ft? (1 acre = \(43,560\mathrm{\ ft}^2\).)
c. The number of plants of a different type follows a Poisson distribution with mean \(\lambda\) plants per acre, where \(\lambda\) is unknown. A total of 5 plants are counted in a 0.1 acre area. Estimate \(\lambda\), and find the uncertainty in the estimate.
Equation Transcription:
Text Transcription:
T
43,560 ft^2
lambda
ANSWER:Solution
Step 1 of 3
Here given the no. of plants in forest has a poisson distribution with mean 10 per acre
Let X represents the no. of plants
The pmf of poisson distribution is P(x) =, x=0,1,2,............
Then Xpoisson(10)
a) Here we have to find the probability that there will be exactly 18 plants in 2 acre
For one acre 10 plants
For 2 acre 20 plants
Hence =20
Now P(x=18)=
=0.0844
Hence the probability that there will be exactly 18 plants in 2 acre is 0.0844