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A river where drinking water is taken is feared to have been polluted by coliform bacteria In order to investigate this, we take a sample tube of water at n randomly selected sites from the river tube and from each of these samples we determine the numbers of coliform bacteria Y₁, . . ., Yn. A classical distribution used to describe the distribution of the number of bacteria per unit volume of water, is the Poisson distribution. So we model our measurement results so that they form a random sample Y₁, ..., Yn from Poisson distribution, i.e. we assume we have n independent observations from the Poisson distribution. In the exercises for Week 1, a statistical model was derived for this model. Now we continue deriving the maximum likelihood estimate in this model. (a) Construct the likelihood function L(\; y) of the model and construct the log- likelihood function ((\; y) of the model (b) Derive by examining the log-likelihood function and carefully justifying the max- imum likelihood estimate of the parameter \

A river where drinking water is taken is feared to have been polluted by coliform bacteria In order to investigate this, we take a sample tube of water at n randomly selected sites from the river tube and from each of these samples we determine the numbers of coliform bacteria Y₁, . . ., Yn. A classical distribution used to describe the distribution of the number of bacteria per unit volume of water, is the Poisson distribution. So we model our measurement results so that they form a random sample Y₁, ..., Yn from Poisson distribution, i.e. we assume we have n independent observations from the Poisson distribution. In the exercises for Week 1, a statistical model was derived for this model. Now we continue deriving the maximum likelihood estimate in this model. (a) Construct the likelihood function L(\; y) of the model and construct the log- likelihood function ((\; y) of the model (b) Derive by examining the log-likelihood function and carefully justifying the max- imum likelihood estimate of the parameter \

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 25SGR
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A river where drinking water is taken is feared to have been polluted by coliform bacteria In order to investigate this, we take a sample tube of water at n randomly selected sites from the river tube and from each of these samples we determine the numbers of coliform bacteria Y₁, . . ., Yn. A classical distribution used to describe the distribution of the number of bacteria per unit volume of water, is the Poisson distribution. So we model our measurement results so that they form a random sample Y₁,..., Y from Poisson distribution, i.e. we assume we have n independent observations from the Poisson distribution. In the exercises for Week 1, a statistical model was derived for this model. Now we continue deriving the maximum likelihood estimate in this model. (a) Construct the likelihood function L(\; y) of the model and construct the log- likelihood function ((\; y) of the model (b) Derive by examining the log-likelihood function and carefully justifying the max- imum likelihood estimate of the parameter >
Transcribed Image Text:A river where drinking water is taken is feared to have been polluted by coliform bacteria In order to investigate this, we take a sample tube of water at n randomly selected sites from the river tube and from each of these samples we determine the numbers of coliform bacteria Y₁, . . ., Yn. A classical distribution used to describe the distribution of the number of bacteria per unit volume of water, is the Poisson distribution. So we model our measurement results so that they form a random sample Y₁,..., Y from Poisson distribution, i.e. we assume we have n independent observations from the Poisson distribution. In the exercises for Week 1, a statistical model was derived for this model. Now we continue deriving the maximum likelihood estimate in this model. (a) Construct the likelihood function L(\; y) of the model and construct the log- likelihood function ((\; y) of the model (b) Derive by examining the log-likelihood function and carefully justifying the max- imum likelihood estimate of the parameter >
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