Suppose that a sequence of mutually independent and identically distributed discrete random variables X₁, X₂, X3, ..., Xn has the following probability density function 0xe-0 x! 0, a) b) c) f(x; 0) = for x = 0,1,2,... elsewhere Show that for any & > 0 and S₂ = ₁ X₁, lim P(|S₁ − 0| ≥ ɛ) = 0. 1 n Zi=1 - n n-8 Show that a statistic Sn in a) is the maximum likelihood estimator of the parameter 8. Let Ô₁ X₁+2X₂+2X3-X4 = 4 ¹ and Ô₂ = ²(X₁ + X₂ + X3 + X4) be two unbiased estimators of 8. Which one of the two estimators is more efficient?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
Suppose that a sequence of mutually independent and identically distributed discrete random
variables X₁, X₂, X3, ..., Xn has the following probability density function
0xe-0
x!
0,
a)
b)
c)
f(x; 0) =
for x = 0,1,2,...
elsewhere
1 n
Show that for any & > 0 and S₂ = ₁X₁, lim P(|S, − 0| ≥ ɛ) = 0.
-
Zi=1
n
n→∞
Show that a statistic Sn in a) is the maximum likelihood estimator of the parameter 8.
Let Ô₁ X₁+2X₂+2X3-X4
=
4
¹ and Ô₂ = ²(X₁ + X₂ + X3 + X4) be two unbiased estimators of 8. Which
one of the two estimators is more efficient?
Transcribed Image Text:Suppose that a sequence of mutually independent and identically distributed discrete random variables X₁, X₂, X3, ..., Xn has the following probability density function 0xe-0 x! 0, a) b) c) f(x; 0) = for x = 0,1,2,... elsewhere 1 n Show that for any & > 0 and S₂ = ₁X₁, lim P(|S, − 0| ≥ ɛ) = 0. - Zi=1 n n→∞ Show that a statistic Sn in a) is the maximum likelihood estimator of the parameter 8. Let Ô₁ X₁+2X₂+2X3-X4 = 4 ¹ and Ô₂ = ²(X₁ + X₂ + X3 + X4) be two unbiased estimators of 8. Which one of the two estimators is more efficient?
Expert Solution
steps

Step by step

Solved in 4 steps with 3 images

Blurred answer
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question

1. What is the Cramer-Rao lower bound for the variance of the unbiased estimator of the parameter ?? 
2. Use the one-parameter regular exponential family definition to find the functions, ℎ(?),?(?),?(?) and ?(?).

Solution
Bartleby Expert
SEE SOLUTION
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