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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.

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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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.
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