Homework Help is Here – Start Your Trial Now!
Math
Statistics
n Show that for any &> 0 and S₁ = 1X₁, lim P(|S₁ - 01 ≥ ) = 0. Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 0. ( Let 0₁ = X₁+2x+2X₁-X₁ and 6₂ = (X₁ + X₂ + X₁ + X₂) be two unbiased estimators of 8. Which one of the two estimators is more efficient?

n Show that for any &> 0 and S₁ = 1X₁, lim P(|S₁ - 01 ≥ ) = 0. Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 0. ( Let 0₁ = X₁+2x+2X₁-X₁ and 6₂ = (X₁ + X₂ + X₁ + X₂) be two unbiased estimators of 8. Which one of the two estimators is more efficient?

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
Suppose that a sequence of mutually independent and identically distributed discrete random variables X₁, X₂, X3,..., X has the following probability density function (0%e-e x! 0. a) b) c) f(x; 0) = for x = 0,1,2,... elsewhere Show that for any > > 0 and S₂ = 1X₁, lim P(|S₁-01 ≥ ) = 0. 348 Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 0. ( Let Ô₁ = X₁+2X²+2X₁-X₁ and ₂ = (X₁ + X₂ + X3 + X4) be two unbiased estimators of 8. Which one of the two estimators is more efficient? d) What is the Cramer-Rao lower bound for the variance of the unbiased estimator of th parameter 8? e) Use the one-parameter regular exponential family definition to find the functions, h(x), c(0), w(0) and t(x).
Transcribed Image Text:Suppose that a sequence of mutually independent and identically distributed discrete random variables X₁, X₂, X3,..., X has the following probability density function (0%e-e x! 0. a) b) c) f(x; 0) = for x = 0,1,2,... elsewhere Show that for any > > 0 and S₂ = 1X₁, lim P(|S₁-01 ≥ ) = 0. 348 Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 0. ( Let Ô₁ = X₁+2X²+2X₁-X₁ and ₂ = (X₁ + X₂ + X3 + X4) be two unbiased estimators of 8. Which one of the two estimators is more efficient? d) What is the Cramer-Rao lower bound for the variance of the unbiased estimator of th parameter 8? e) Use the one-parameter regular exponential family definition to find the functions, h(x), c(0), w(0) and t(x).
Expert Solution
steps

Step by step

Solved in 5 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
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