SlideShare a Scribd company logo
Let X1,,Xn be i.i.d. from N(,1) and let U1,,Un be i.i.d. from U(0,1). All the 2n random variables
are independent. Let Yi=XiUi,i=1,,n. If the Xi and Ui are both observed, then X would be a
natural estimator for . If only the products Y1,,Yn are observed, then 2Y may be a reasonable
estimator for . Show that both X and Y are unbiased estimators for and determine the relative
efficiency of 2Y with respect to X.

More Related Content

More from info532468

Listmann Corp. processes four different products that can either be s.pdf
 Listmann Corp. processes four different products that can either be s.pdf Listmann Corp. processes four different products that can either be s.pdf
Listmann Corp. processes four different products that can either be s.pdf
info532468
 
Let 719 represent an interval on the number line. Complete parts (a.pdf
 Let 719 represent an interval on the number line. Complete parts (a.pdf Let 719 represent an interval on the number line. Complete parts (a.pdf
Let 719 represent an interval on the number line. Complete parts (a.pdf
info532468
 
lernatoglyphia is a rare, doninant condition where people are born wi.pdf
 lernatoglyphia is a rare, doninant condition where people are born wi.pdf lernatoglyphia is a rare, doninant condition where people are born wi.pdf
lernatoglyphia is a rare, doninant condition where people are born wi.pdf
info532468
 
Let Y1,�,Yn be i.i.d. random variables with YiN(,). Instead of using .pdf
 Let Y1,�,Yn be i.i.d. random variables with YiN(,). Instead of using .pdf Let Y1,�,Yn be i.i.d. random variables with YiN(,). Instead of using .pdf
Let Y1,�,Yn be i.i.d. random variables with YiN(,). Instead of using .pdf
info532468
 
Let Y be a random variable, In a population, Y=147 and of Y2=50. Use .pdf
 Let Y be a random variable, In a population, Y=147 and of Y2=50. Use .pdf Let Y be a random variable, In a population, Y=147 and of Y2=50. Use .pdf
Let Y be a random variable, In a population, Y=147 and of Y2=50. Use .pdf
info532468
 
Let Y be a random variable with the following frobability distributio.pdf
 Let Y be a random variable with the following frobability distributio.pdf Let Y be a random variable with the following frobability distributio.pdf
Let Y be a random variable with the following frobability distributio.pdf
info532468
 
Let X1,�,Xn be i.i.d. random variables from normal distribution with .pdf
 Let X1,�,Xn be i.i.d. random variables from normal distribution with .pdf Let X1,�,Xn be i.i.d. random variables from normal distribution with .pdf
Let X1,�,Xn be i.i.d. random variables from normal distribution with .pdf
info532468
 
Module 11 Discussion Postinn outide the ansigsed dicution wil not cou.pdf
 Module 11 Discussion Postinn outide the ansigsed dicution wil not cou.pdf Module 11 Discussion Postinn outide the ansigsed dicution wil not cou.pdf
Module 11 Discussion Postinn outide the ansigsed dicution wil not cou.pdf
info532468
 
Ministry of Health guidelines to protect yourself from Covid-19. 1. C.pdf
 Ministry of Health guidelines to protect yourself from Covid-19. 1. C.pdf Ministry of Health guidelines to protect yourself from Covid-19. 1. C.pdf
Ministry of Health guidelines to protect yourself from Covid-19. 1. C.pdf
info532468
 
Left to Right Shunts y If the SYSIEMIC (SVR) is greater than the Vas.pdf
 Left to Right Shunts y If the SYSIEMIC (SVR) is greater than the Vas.pdf Left to Right Shunts y If the SYSIEMIC (SVR) is greater than the Vas.pdf
Left to Right Shunts y If the SYSIEMIC (SVR) is greater than the Vas.pdf
info532468
 
Learn Terminology Read Gervais chapters 8 and 9 . Define each of the .pdf
 Learn Terminology Read Gervais chapters 8 and 9 . Define each of the .pdf Learn Terminology Read Gervais chapters 8 and 9 . Define each of the .pdf
Learn Terminology Read Gervais chapters 8 and 9 . Define each of the .pdf
info532468
 
Microaerophiles means A. relatively smaller bacteria that grow .pdf
 Microaerophiles means A. relatively smaller bacteria that grow .pdf Microaerophiles means A. relatively smaller bacteria that grow .pdf
Microaerophiles means A. relatively smaller bacteria that grow .pdf
info532468
 
Mesuradewn Cerpeasa. Prepare a flexible budget for the actual unit.pdf
 Mesuradewn Cerpeasa. Prepare a flexible budget for the actual unit.pdf Mesuradewn Cerpeasa. Prepare a flexible budget for the actual unit.pdf
Mesuradewn Cerpeasa. Prepare a flexible budget for the actual unit.pdf
info532468
 
Leaders successfully create a shared sense of purpose (i.e., a common.pdf
 Leaders successfully create a shared sense of purpose (i.e., a common.pdf Leaders successfully create a shared sense of purpose (i.e., a common.pdf
Leaders successfully create a shared sense of purpose (i.e., a common.pdf
info532468
 
Leanne made ordinary annuity payments of $351 per month for fourteen .pdf
 Leanne made ordinary annuity payments of $351 per month for fourteen .pdf Leanne made ordinary annuity payments of $351 per month for fourteen .pdf
Leanne made ordinary annuity payments of $351 per month for fourteen .pdf
info532468
 
Medical Specialities The following doctors were observed on staff at .pdf
 Medical Specialities The following doctors were observed on staff at .pdf Medical Specialities The following doctors were observed on staff at .pdf
Medical Specialities The following doctors were observed on staff at .pdf
info532468
 
MCQs [5 Marks] 1. The basic functions that a computer should have ca.pdf
 MCQs [5 Marks] 1. The basic functions that a computer should have ca.pdf MCQs [5 Marks] 1. The basic functions that a computer should have ca.pdf
MCQs [5 Marks] 1. The basic functions that a computer should have ca.pdf
info532468
 
Mayfair Company completed the following transactions and uses a perpe.pdf
 Mayfair Company completed the following transactions and uses a perpe.pdf Mayfair Company completed the following transactions and uses a perpe.pdf
Mayfair Company completed the following transactions and uses a perpe.pdf
info532468
 
Matthew Finley wishes to become a millionaire. His money market fund .pdf
 Matthew Finley wishes to become a millionaire. His money market fund .pdf Matthew Finley wishes to become a millionaire. His money market fund .pdf
Matthew Finley wishes to become a millionaire. His money market fund .pdf
info532468
 
Matching Match each system with its component. (5 points) 1. Circula.pdf
 Matching Match each system with its component. (5 points) 1. Circula.pdf Matching Match each system with its component. (5 points) 1. Circula.pdf
Matching Match each system with its component. (5 points) 1. Circula.pdf
info532468
 

More from info532468 (20)

Listmann Corp. processes four different products that can either be s.pdf
 Listmann Corp. processes four different products that can either be s.pdf Listmann Corp. processes four different products that can either be s.pdf
Listmann Corp. processes four different products that can either be s.pdf
 
Let 719 represent an interval on the number line. Complete parts (a.pdf
 Let 719 represent an interval on the number line. Complete parts (a.pdf Let 719 represent an interval on the number line. Complete parts (a.pdf
Let 719 represent an interval on the number line. Complete parts (a.pdf
 
lernatoglyphia is a rare, doninant condition where people are born wi.pdf
 lernatoglyphia is a rare, doninant condition where people are born wi.pdf lernatoglyphia is a rare, doninant condition where people are born wi.pdf
lernatoglyphia is a rare, doninant condition where people are born wi.pdf
 
Let Y1,�,Yn be i.i.d. random variables with YiN(,). Instead of using .pdf
 Let Y1,�,Yn be i.i.d. random variables with YiN(,). Instead of using .pdf Let Y1,�,Yn be i.i.d. random variables with YiN(,). Instead of using .pdf
Let Y1,�,Yn be i.i.d. random variables with YiN(,). Instead of using .pdf
 
Let Y be a random variable, In a population, Y=147 and of Y2=50. Use .pdf
 Let Y be a random variable, In a population, Y=147 and of Y2=50. Use .pdf Let Y be a random variable, In a population, Y=147 and of Y2=50. Use .pdf
Let Y be a random variable, In a population, Y=147 and of Y2=50. Use .pdf
 
Let Y be a random variable with the following frobability distributio.pdf
 Let Y be a random variable with the following frobability distributio.pdf Let Y be a random variable with the following frobability distributio.pdf
Let Y be a random variable with the following frobability distributio.pdf
 
Let X1,�,Xn be i.i.d. random variables from normal distribution with .pdf
 Let X1,�,Xn be i.i.d. random variables from normal distribution with .pdf Let X1,�,Xn be i.i.d. random variables from normal distribution with .pdf
Let X1,�,Xn be i.i.d. random variables from normal distribution with .pdf
 
Module 11 Discussion Postinn outide the ansigsed dicution wil not cou.pdf
 Module 11 Discussion Postinn outide the ansigsed dicution wil not cou.pdf Module 11 Discussion Postinn outide the ansigsed dicution wil not cou.pdf
Module 11 Discussion Postinn outide the ansigsed dicution wil not cou.pdf
 
Ministry of Health guidelines to protect yourself from Covid-19. 1. C.pdf
 Ministry of Health guidelines to protect yourself from Covid-19. 1. C.pdf Ministry of Health guidelines to protect yourself from Covid-19. 1. C.pdf
Ministry of Health guidelines to protect yourself from Covid-19. 1. C.pdf
 
Left to Right Shunts y If the SYSIEMIC (SVR) is greater than the Vas.pdf
 Left to Right Shunts y If the SYSIEMIC (SVR) is greater than the Vas.pdf Left to Right Shunts y If the SYSIEMIC (SVR) is greater than the Vas.pdf
Left to Right Shunts y If the SYSIEMIC (SVR) is greater than the Vas.pdf
 
Learn Terminology Read Gervais chapters 8 and 9 . Define each of the .pdf
 Learn Terminology Read Gervais chapters 8 and 9 . Define each of the .pdf Learn Terminology Read Gervais chapters 8 and 9 . Define each of the .pdf
Learn Terminology Read Gervais chapters 8 and 9 . Define each of the .pdf
 
Microaerophiles means A. relatively smaller bacteria that grow .pdf
 Microaerophiles means A. relatively smaller bacteria that grow .pdf Microaerophiles means A. relatively smaller bacteria that grow .pdf
Microaerophiles means A. relatively smaller bacteria that grow .pdf
 
Mesuradewn Cerpeasa. Prepare a flexible budget for the actual unit.pdf
 Mesuradewn Cerpeasa. Prepare a flexible budget for the actual unit.pdf Mesuradewn Cerpeasa. Prepare a flexible budget for the actual unit.pdf
Mesuradewn Cerpeasa. Prepare a flexible budget for the actual unit.pdf
 
Leaders successfully create a shared sense of purpose (i.e., a common.pdf
 Leaders successfully create a shared sense of purpose (i.e., a common.pdf Leaders successfully create a shared sense of purpose (i.e., a common.pdf
Leaders successfully create a shared sense of purpose (i.e., a common.pdf
 
Leanne made ordinary annuity payments of $351 per month for fourteen .pdf
 Leanne made ordinary annuity payments of $351 per month for fourteen .pdf Leanne made ordinary annuity payments of $351 per month for fourteen .pdf
Leanne made ordinary annuity payments of $351 per month for fourteen .pdf
 
Medical Specialities The following doctors were observed on staff at .pdf
 Medical Specialities The following doctors were observed on staff at .pdf Medical Specialities The following doctors were observed on staff at .pdf
Medical Specialities The following doctors were observed on staff at .pdf
 
MCQs [5 Marks] 1. The basic functions that a computer should have ca.pdf
 MCQs [5 Marks] 1. The basic functions that a computer should have ca.pdf MCQs [5 Marks] 1. The basic functions that a computer should have ca.pdf
MCQs [5 Marks] 1. The basic functions that a computer should have ca.pdf
 
Mayfair Company completed the following transactions and uses a perpe.pdf
 Mayfair Company completed the following transactions and uses a perpe.pdf Mayfair Company completed the following transactions and uses a perpe.pdf
Mayfair Company completed the following transactions and uses a perpe.pdf
 
Matthew Finley wishes to become a millionaire. His money market fund .pdf
 Matthew Finley wishes to become a millionaire. His money market fund .pdf Matthew Finley wishes to become a millionaire. His money market fund .pdf
Matthew Finley wishes to become a millionaire. His money market fund .pdf
 
Matching Match each system with its component. (5 points) 1. Circula.pdf
 Matching Match each system with its component. (5 points) 1. Circula.pdf Matching Match each system with its component. (5 points) 1. Circula.pdf
Matching Match each system with its component. (5 points) 1. Circula.pdf
 

Recently uploaded

2024.06.01 Introducing a competency framework for languag learning materials ...
2024.06.01 Introducing a competency framework for languag learning materials ...2024.06.01 Introducing a competency framework for languag learning materials ...
2024.06.01 Introducing a competency framework for languag learning materials ...
Sandy Millin
 
Synthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptxSynthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptx
Pavel ( NSTU)
 
Polish students' mobility in the Czech Republic
Polish students' mobility in the Czech RepublicPolish students' mobility in the Czech Republic
Polish students' mobility in the Czech Republic
Anna Sz.
 
Embracing GenAI - A Strategic Imperative
Embracing GenAI - A Strategic ImperativeEmbracing GenAI - A Strategic Imperative
Embracing GenAI - A Strategic Imperative
Peter Windle
 
Francesca Gottschalk - How can education support child empowerment.pptx
Francesca Gottschalk - How can education support child empowerment.pptxFrancesca Gottschalk - How can education support child empowerment.pptx
Francesca Gottschalk - How can education support child empowerment.pptx
EduSkills OECD
 
The basics of sentences session 5pptx.pptx
The basics of sentences session 5pptx.pptxThe basics of sentences session 5pptx.pptx
The basics of sentences session 5pptx.pptx
heathfieldcps1
 
The Challenger.pdf DNHS Official Publication
The Challenger.pdf DNHS Official PublicationThe Challenger.pdf DNHS Official Publication
The Challenger.pdf DNHS Official Publication
Delapenabediema
 
Biological Screening of Herbal Drugs in detailed.
Biological Screening of Herbal Drugs in detailed.Biological Screening of Herbal Drugs in detailed.
Biological Screening of Herbal Drugs in detailed.
Ashokrao Mane college of Pharmacy Peth-Vadgaon
 
Model Attribute Check Company Auto Property
Model Attribute  Check Company Auto PropertyModel Attribute  Check Company Auto Property
Model Attribute Check Company Auto Property
Celine George
 
678020731-Sumas-y-Restas-Para-Colorear.pdf
678020731-Sumas-y-Restas-Para-Colorear.pdf678020731-Sumas-y-Restas-Para-Colorear.pdf
678020731-Sumas-y-Restas-Para-Colorear.pdf
CarlosHernanMontoyab2
 
Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf
Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdfAdversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf
Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf
Po-Chuan Chen
 
A Strategic Approach: GenAI in Education
A Strategic Approach: GenAI in EducationA Strategic Approach: GenAI in Education
A Strategic Approach: GenAI in Education
Peter Windle
 
Sha'Carri Richardson Presentation 202345
Sha'Carri Richardson Presentation 202345Sha'Carri Richardson Presentation 202345
Sha'Carri Richardson Presentation 202345
beazzy04
 
How to Make a Field invisible in Odoo 17
How to Make a Field invisible in Odoo 17How to Make a Field invisible in Odoo 17
How to Make a Field invisible in Odoo 17
Celine George
 
Guidance_and_Counselling.pdf B.Ed. 4th Semester
Guidance_and_Counselling.pdf B.Ed. 4th SemesterGuidance_and_Counselling.pdf B.Ed. 4th Semester
Guidance_and_Counselling.pdf B.Ed. 4th Semester
Atul Kumar Singh
 
"Protectable subject matters, Protection in biotechnology, Protection of othe...
"Protectable subject matters, Protection in biotechnology, Protection of othe..."Protectable subject matters, Protection in biotechnology, Protection of othe...
"Protectable subject matters, Protection in biotechnology, Protection of othe...
SACHIN R KONDAGURI
 
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
Levi Shapiro
 
Home assignment II on Spectroscopy 2024 Answers.pdf
Home assignment II on Spectroscopy 2024 Answers.pdfHome assignment II on Spectroscopy 2024 Answers.pdf
Home assignment II on Spectroscopy 2024 Answers.pdf
Tamralipta Mahavidyalaya
 
1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx
JosvitaDsouza2
 
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdf
Welcome to TechSoup   New Member Orientation and Q&A (May 2024).pdfWelcome to TechSoup   New Member Orientation and Q&A (May 2024).pdf
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdf
TechSoup
 

Recently uploaded (20)

2024.06.01 Introducing a competency framework for languag learning materials ...
2024.06.01 Introducing a competency framework for languag learning materials ...2024.06.01 Introducing a competency framework for languag learning materials ...
2024.06.01 Introducing a competency framework for languag learning materials ...
 
Synthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptxSynthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptx
 
Polish students' mobility in the Czech Republic
Polish students' mobility in the Czech RepublicPolish students' mobility in the Czech Republic
Polish students' mobility in the Czech Republic
 
Embracing GenAI - A Strategic Imperative
Embracing GenAI - A Strategic ImperativeEmbracing GenAI - A Strategic Imperative
Embracing GenAI - A Strategic Imperative
 
Francesca Gottschalk - How can education support child empowerment.pptx
Francesca Gottschalk - How can education support child empowerment.pptxFrancesca Gottschalk - How can education support child empowerment.pptx
Francesca Gottschalk - How can education support child empowerment.pptx
 
The basics of sentences session 5pptx.pptx
The basics of sentences session 5pptx.pptxThe basics of sentences session 5pptx.pptx
The basics of sentences session 5pptx.pptx
 
The Challenger.pdf DNHS Official Publication
The Challenger.pdf DNHS Official PublicationThe Challenger.pdf DNHS Official Publication
The Challenger.pdf DNHS Official Publication
 
Biological Screening of Herbal Drugs in detailed.
Biological Screening of Herbal Drugs in detailed.Biological Screening of Herbal Drugs in detailed.
Biological Screening of Herbal Drugs in detailed.
 
Model Attribute Check Company Auto Property
Model Attribute  Check Company Auto PropertyModel Attribute  Check Company Auto Property
Model Attribute Check Company Auto Property
 
678020731-Sumas-y-Restas-Para-Colorear.pdf
678020731-Sumas-y-Restas-Para-Colorear.pdf678020731-Sumas-y-Restas-Para-Colorear.pdf
678020731-Sumas-y-Restas-Para-Colorear.pdf
 
Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf
Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdfAdversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf
Adversarial Attention Modeling for Multi-dimensional Emotion Regression.pdf
 
A Strategic Approach: GenAI in Education
A Strategic Approach: GenAI in EducationA Strategic Approach: GenAI in Education
A Strategic Approach: GenAI in Education
 
Sha'Carri Richardson Presentation 202345
Sha'Carri Richardson Presentation 202345Sha'Carri Richardson Presentation 202345
Sha'Carri Richardson Presentation 202345
 
How to Make a Field invisible in Odoo 17
How to Make a Field invisible in Odoo 17How to Make a Field invisible in Odoo 17
How to Make a Field invisible in Odoo 17
 
Guidance_and_Counselling.pdf B.Ed. 4th Semester
Guidance_and_Counselling.pdf B.Ed. 4th SemesterGuidance_and_Counselling.pdf B.Ed. 4th Semester
Guidance_and_Counselling.pdf B.Ed. 4th Semester
 
"Protectable subject matters, Protection in biotechnology, Protection of othe...
"Protectable subject matters, Protection in biotechnology, Protection of othe..."Protectable subject matters, Protection in biotechnology, Protection of othe...
"Protectable subject matters, Protection in biotechnology, Protection of othe...
 
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
 
Home assignment II on Spectroscopy 2024 Answers.pdf
Home assignment II on Spectroscopy 2024 Answers.pdfHome assignment II on Spectroscopy 2024 Answers.pdf
Home assignment II on Spectroscopy 2024 Answers.pdf
 
1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx
 
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdf
Welcome to TechSoup   New Member Orientation and Q&A (May 2024).pdfWelcome to TechSoup   New Member Orientation and Q&A (May 2024).pdf
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdf
 

Let X1,�,Xn be i.i.d. from N(,1) and let U1,�,Un be i.i.d. from U(0,1.pdf

  • 1. Let X1,,Xn be i.i.d. from N(,1) and let U1,,Un be i.i.d. from U(0,1). All the 2n random variables are independent. Let Yi=XiUi,i=1,,n. If the Xi and Ui are both observed, then X would be a natural estimator for . If only the products Y1,,Yn are observed, then 2Y may be a reasonable estimator for . Show that both X and Y are unbiased estimators for and determine the relative efficiency of 2Y with respect to X.