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An experimenter wishes to compare the numbers of bacteria of types A and B in samples of water. A total of n independent water samples are taken, and counts are made for each sample. Let X, denote the number of type A bacteria and Y; denote the number of type B bacteria for sample i. Assume that the two bacteria types are sparsely distributed within a water sample so that X₁, X₂, . . . , X₁ and Y₁, Y2, . " Yn can be considered independent random samples from Poisson distributions with means X₁ and A2, respectively. Suggest an estimator of A₁/(₁+ λ₂). What properties does your estimator have?

An experimenter wishes to compare the numbers of bacteria of types A and B in samples of water. A total of n independent water samples are taken, and counts are made for each sample. Let X, denote the number of type A bacteria and Y; denote the number of type B bacteria for sample i. Assume that the two bacteria types are sparsely distributed within a water sample so that X₁, X₂, . . . , X₁ and Y₁, Y2, . " Yn can be considered independent random samples from Poisson distributions with means X₁ and A2, respectively. Suggest an estimator of A₁/(₁+ λ₂). What properties does your estimator have?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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An experimenter wishes to compare the numbers of bacteria of types A and B in samples of water. A total of n independent water samples are taken, and counts are made for each sample. Let X, denote the number of type A bacteria and Y; denote the number of type B bacteria for sample i. Assume that the two bacteria types are sparsely distributed within a water sample so that X₁, X2, . . . Xn and Y₁, Y2,. " Yn can be considered independent random samples from Poisson distributions with means X₁ and X2, respectively. Suggest an estimator of A₁/(\₁ + A₂). What properties does your estimator have?
Transcribed Image Text:An experimenter wishes to compare the numbers of bacteria of types A and B in samples of water. A total of n independent water samples are taken, and counts are made for each sample. Let X, denote the number of type A bacteria and Y; denote the number of type B bacteria for sample i. Assume that the two bacteria types are sparsely distributed within a water sample so that X₁, X2, . . . Xn and Y₁, Y2,. " Yn can be considered independent random samples from Poisson distributions with means X₁ and X2, respectively. Suggest an estimator of A₁/(\₁ + A₂). What properties does your estimator have?
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