Grasshoppers are distributed at random in a large field according to a Poisson p
ID: 3220989 • Letter: G
Question
Grasshoppers are distributed at random in a large field according to a Poisson process. A research assistant (RA) for the entomology department is given the task of analyzing the density of grasshoppers in a field. (a) The RA find 123 grasshoppers over 60 square meters. Estimate the expected number of grasshoppers per square meter and give the uncertainty for the estimate. (b) What is the estimated probability of finding 0 grasshoppers per square meter? Round to four decimal places. (c) What is the estimated probability of finding 10 grasshoppers per 5 square meters? Round to four decimal places.Explanation / Answer
(a)
123 grasshopers over 60 square meters
Hence 123/60 = 2.05 grasshopers per square meter
uncertainity of estimate = sqrt(2.05) = 1.4318
(b)
P(X=0) = (2.05)^0 * e^(-2.05)/0! = 0.1287
Hence 0.1287 is the probability of finding 0 grasshopers per square meter.
(c)
2.05*5 = 10.25 grasshoppers per 5 square meters
P(X=10) (10.25)^10 * e^(-10.25)/10! = 0.1247
Hence 0.1247 is the probability of finding 10 grasshoppers per 5 square meters
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