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
6th Edition
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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Problem 1P
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe60e14a8-856f-447c-ac90-795ae43e00b4%2F0bd1ff9f-37d4-4736-b6c1-d900ac7f07c5%2Ff578mqi_processed.png&w=3840&q=75)
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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