22. Let X denote the proportion of allotted time that a ran- domly selected student spends working on a certain aptitude test. Suppose the pdf of X is f(x; 0) = [ (0 + 1)x° 0 ≤ x ≤1 0 otherwise where -1 <0. A random sample of ten students yields data x₁ = .92, x2 = .79, x3= .90, x4 = .65, x = .86, x = .47, x7 = .73, x = .97, x = .94, x10 = .77. a. Use the method of moments to obtain an estimator of A, and then compute the estimate for this data. b. Obtain the maximum likelihood estimator of 0, and then compute the estimate for the given data.

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
22. Let X denote the proportion of allotted time that a ran-
domly selected student spends working on a certain
aptitude test. Suppose the pdf of X is
f(x; 0)
=
[ (0 + 1)x° 0 ≤ x ≤1
0
otherwise
where -1 <0. A random sample of ten students yields
data x₁ = .92, x2 = .79, x3= .90, x4 = .65, x = .86,
x = .47, x7 = .73, x = .97, x = .94, x10 = .77.
a. Use the method of moments to obtain an estimator of
A, and then compute the estimate for this data.
b. Obtain the maximum likelihood estimator of 0, and
then compute the estimate for the given data.
Transcribed Image Text:22. Let X denote the proportion of allotted time that a ran- domly selected student spends working on a certain aptitude test. Suppose the pdf of X is f(x; 0) = [ (0 + 1)x° 0 ≤ x ≤1 0 otherwise where -1 <0. A random sample of ten students yields data x₁ = .92, x2 = .79, x3= .90, x4 = .65, x = .86, x = .47, x7 = .73, x = .97, x = .94, x10 = .77. a. Use the method of moments to obtain an estimator of A, and then compute the estimate for this data. b. Obtain the maximum likelihood estimator of 0, and then compute the estimate for the given data.
Expert Solution
steps

Step by step

Solved in 2 steps

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