Homework Help is Here – Start Your Trial Now!
Math
Statistics
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. (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 > (c) Show with justifications that the ML estimator of the model is unbiased (d) Calculate the mean squared error msex A(^(Y)) of the ML estimator of the model

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. (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 > (c) Show with justifications that the ML estimator of the model is unbiased (d) Calculate the mean squared error msex A(^(Y)) of the ML estimator of the model

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
See similar textbooks
icon
Related questions
Question
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. (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 (c) Show with justifications that the ML estimator of the model is unbiased (d) Calculate the mean squared error msex (^(Y)) of the ML estimator of the model
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,..., Yn from Poisson distribution, i.e. we assume we have n independent observations from the Poisson distribution. (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 (c) Show with justifications that the ML estimator of the model is unbiased (d) Calculate the mean squared error msex (^(Y)) of the ML estimator of the model
Expert Solution
steps

Step by step

Solved in 5 steps with 17 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
SEE MORE TEXTBOOKS