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5. We have data on the number of animals per quadrat in a study area. In particular, over n quadrats or minutes, we obtain counts ₁, 2,..., In that are independent. If the settling or arrival process is random, the data are from a Poisson distribution with pmf: where A> 0 and x = 0, 1,... (a) Show that the likelihood is p(x) = (b) Show that the log-likelihood is e-√√² x! n L(X; ₁, 2,...,n) = II i=1 e-11² x¡! 12 ((X;F1,72, ... ,Χn) = log(3) Σπ; - ηλ - -Σlog(x;!) i=1 i=1 n (c) Using the first and second derivatives for find the maximum likehood estimates for A and its 95% confidence interval (CI).

5. We have data on the number of animals per quadrat in a study area. In particular, over n quadrats or minutes, we obtain counts ₁, 2,..., In that are independent. If the settling or arrival process is random, the data are from a Poisson distribution with pmf: where A> 0 and x = 0, 1,... (a) Show that the likelihood is p(x) = (b) Show that the log-likelihood is e-√√² x! n L(X; ₁, 2,...,n) = II i=1 e-11² x¡! 12 ((X;F1,72, ... ,Χn) = log(3) Σπ; - ηλ - -Σlog(x;!) i=1 i=1 n (c) Using the first and second derivatives for find the maximum likehood estimates for A and its 95% confidence interval (CI).

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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5. We have data on the number of animals per quadrat in a study area. In particular, over n quadrats or minutes, we obtain counts ₁, 2,..., In that are independent. If the settling or arrival process is random, the data are from a Poisson distribution with pmf: where A> 0 and x = 0, 1,... (a) Show that the likelihood is p(x) = (b) Show that the log-likelihood is e-√√² x! n L(X; ₁, 2,...,n) = II i=1 e-11² x¡! 12 ((X;F1,72, ... ,Χn) = log(3) Σπ; - ηλ - -Σlog(x;!) i=1 i=1 n (c) Using the first and second derivatives for & find the maximum likehood estimates for A and its 95% confidence interval (CI).
Transcribed Image Text:5. We have data on the number of animals per quadrat in a study area. In particular, over n quadrats or minutes, we obtain counts ₁, 2,..., In that are independent. If the settling or arrival process is random, the data are from a Poisson distribution with pmf: where A> 0 and x = 0, 1,... (a) Show that the likelihood is p(x) = (b) Show that the log-likelihood is e-√√² x! n L(X; ₁, 2,...,n) = II i=1 e-11² x¡! 12 ((X;F1,72, ... ,Χn) = log(3) Σπ; - ηλ - -Σlog(x;!) i=1 i=1 n (c) Using the first and second derivatives for & find the maximum likehood estimates for A and its 95% confidence interval (CI).
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