Homework Help is Here – Start Your Trial Now!
Math
Statistics
Let X1, .., Xn be a random sample from a population with 0 unknown and given by the density = * itz>0 { e f(x; 8) if x < 0 202 and E(X) = 0 (Hint: you may use that e-² za-1dz = Show that E(X) (a – 1)! for every a E N). 1. 2. Show that the statistic (1) n i=1 is an unbiased estimator of 0. 3. Give the definition of a consistent estimator. 4. Show that the estimator 0n given in relation (1) is a consistent estimator of 0. 5. Show that the estimator 0, is a minimum variance estimator of 0. (Hint: use the Cramer-Rao inequality given by 1 var(0) > (Ə ln(f(X;0) nE

Let X1, .., Xn be a random sample from a population with 0 unknown and given by the density = * itz>0 { e f(x; 8) if x < 0 202 and E(X) = 0 (Hint: you may use that e-² za-1dz = Show that E(X) (a – 1)! for every a E N). 1. 2. Show that the statistic (1) n i=1 is an unbiased estimator of 0. 3. Give the definition of a consistent estimator. 4. Show that the estimator 0n given in relation (1) is a consistent estimator of 0. 5. Show that the estimator 0, is a minimum variance estimator of 0. (Hint: use the Cramer-Rao inequality given by 1 var(0) > (Ə ln(f(X;0) nE

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
Let X1, .., Xn be a random sample from a population with 0 unknown and given by the density = * itz>0 { e f(x; 8) if x < 0 202 and E(X) = 0 (Hint: you may use that e-² za-1dz = Show that E(X) (a – 1)! for every a E N). 1. 2. Show that the statistic (1) n i=1 is an unbiased estimator of 0. 3. Give the definition of a consistent estimator. 4. Show that the estimator 0n given in relation (1) is a consistent estimator of 0. 5. Show that the estimator 0, is a minimum variance estimator of 0. (Hint: use the Cramer-Rao inequality given by 1 var(0) > (Ə ln(f(X;0) nE
Transcribed Image Text:Let X1, .., Xn be a random sample from a population with 0 unknown and given by the density = * itz>0 { e f(x; 8) if x < 0 202 and E(X) = 0 (Hint: you may use that e-² za-1dz = Show that E(X) (a – 1)! for every a E N). 1. 2. Show that the statistic (1) n i=1 is an unbiased estimator of 0. 3. Give the definition of a consistent estimator. 4. Show that the estimator 0n given in relation (1) is a consistent estimator of 0. 5. Show that the estimator 0, is a minimum variance estimator of 0. (Hint: use the Cramer-Rao inequality given by 1 var(0) > (Ə ln(f(X;0) nE
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 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