Two-dimensional Poisson process. The number of plants of a certain species in a certain
Chapter 4, Problem 12(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 \(10 T\) .
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?
\(\left(1 \text { acre }=43,560 \mathrm{ft}^{2}\right)\)
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:
10T
(1 acre=43,560 ft2)
\lambda
\lambda
\lambda
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