27. Let X denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test. Suppose the pdf of X is f(x; 0) = (0+1)xº 0≤x≤1 for some > -1. A random sample of ten students yields data x₁ = .92, x₂ = .79, X3 = .90, X4 = .65, x5 = .86, x6 = .47, X7 = .73, x8 = .97, x9 = .94, X10 = .77. a. Use the method of moments to obtain an estimator of 0, and then compute the estimate for this data. b. Obtain the maximum likelihood esti- mator of 0, and then compute the esti- mate for the given data.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
icon
Related questions
Question
27. Let X denote the proportion of allotted time
that a randomly selected student spends
working on a certain aptitude test. Suppose
the pdf of X is
f(x; 0) = (0+1)xº 0≤x≤1
for some > -1. A random sample of ten
students yields data x₁ = .92, x₂ = .79,
X3 = .90, X4 = .65, x5 = .86, x6 = .47,
X7 = .73, x8 = .97, x9 = .94, X10 = .77.
a. Use the method of moments to obtain an
estimator of 0, and then compute the
estimate for this data.
b. Obtain the maximum likelihood esti-
mator of 0, and then compute the esti-
mate for the given data.
Transcribed Image Text:27. Let X denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test. Suppose the pdf of X is f(x; 0) = (0+1)xº 0≤x≤1 for some > -1. A random sample of ten students yields data x₁ = .92, x₂ = .79, X3 = .90, X4 = .65, x5 = .86, x6 = .47, X7 = .73, x8 = .97, x9 = .94, X10 = .77. a. Use the method of moments to obtain an estimator of 0, and then compute the estimate for this data. b. Obtain the maximum likelihood esti- mator of 0, and then compute the esti- mate for the given data.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 1 images

Blurred answer
Similar questions
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON