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

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
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
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS