Homework Help is Here – Start Your Trial Now!
Math
Probability
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)x® where -1 < 8. A random sample of ten students yields data x₁ = 0.86, x₂ = 0.92, x3 = 0.95, x4 = 0.94, X5 = 0.45, x6 = 0.65, x = 0.73, xg = 0.90, x9 = 0.79, X10 = 0.79. (a) Use the method of moments to obtain an estimator of Ⓒ 1 (1 + X) 1 0 (x - 1) - 0 (1 + 7) - 1 1 0 (1-7) - - 2 -n ΣIn(X) Eln(X;) n 2 1 0 (7-1) - Compute the estimate for this data. (Round your answer to two decimal places.) 0≤x≤ 1 otherwise 1 (b) Obtain the maximum likelihood estimator of 0. Eln(X;) n ΣIn(X;) -n - 1 1 n ΣIn(X;) Compute the estimate for the given data. (Round your answer to two decimal places.)

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)x® where -1 < 8. A random sample of ten students yields data x₁ = 0.86, x₂ = 0.92, x3 = 0.95, x4 = 0.94, X5 = 0.45, x6 = 0.65, x = 0.73, xg = 0.90, x9 = 0.79, X10 = 0.79. (a) Use the method of moments to obtain an estimator of Ⓒ 1 (1 + X) 1 0 (x - 1) - 0 (1 + 7) - 1 1 0 (1-7) - - 2 -n ΣIn(X) Eln(X;) n 2 1 0 (7-1) - Compute the estimate for this data. (Round your answer to two decimal places.) 0≤x≤ 1 otherwise 1 (b) Obtain the maximum likelihood estimator of 0. Eln(X;) n ΣIn(X;) -n - 1 1 n ΣIn(X;) Compute the estimate for the given data. (Round your answer to two decimal places.)

A First Course in Probability (10th Edition)
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...
See similar textbooks
icon
Related questions
Question
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)x where -1 < 0. A random sample of ten students yields data x₁ = 0.86, x₂ = 0.92, x3 = 0.95, x4 = 0.94, X5 = 0.45, x6 = 0.65, x = 0.73, xg = 0.90, x9 = 0.79, X10 = 0.79. (a) Use the method of moments to obtain an estimator of Ⓒ 1 (1 + X) - 1 1 0 (x - 1) - - 2 0 (1-7) - -n ΣIn(X) Eln(X;) n 2 0 (1 + 7) 1 0 (7-1) - Compute the estimate for this data. (Round your answer to two decimal places.) 0≤x≤ 1 otherwise 1 (b) Obtain the maximum likelihood estimator of 0. Eln(X;) n ΣΙn(Χ;) -n - 1 1 n ΣIn(Χ.) Compute the estimate for the given data. (Round your answer to two decimal places.)
Transcribed Image Text: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)x where -1 < 0. A random sample of ten students yields data x₁ = 0.86, x₂ = 0.92, x3 = 0.95, x4 = 0.94, X5 = 0.45, x6 = 0.65, x = 0.73, xg = 0.90, x9 = 0.79, X10 = 0.79. (a) Use the method of moments to obtain an estimator of Ⓒ 1 (1 + X) - 1 1 0 (x - 1) - - 2 0 (1-7) - -n ΣIn(X) Eln(X;) n 2 0 (1 + 7) 1 0 (7-1) - Compute the estimate for this data. (Round your answer to two decimal places.) 0≤x≤ 1 otherwise 1 (b) Obtain the maximum likelihood estimator of 0. Eln(X;) n ΣΙn(Χ;) -n - 1 1 n ΣIn(Χ.) Compute the estimate for the given data. (Round your answer to two decimal places.)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 6 steps with 6 images

SEE SOLUTIONCheck out a sample Q&A here
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
SEE MORE TEXTBOOKS