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Let X denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test. Suppose the pdf of Xis +1)x F(x; 6) = 0 otherwise where -1 <0. A random sample of ten students yields data x₁ = 0.65, x₂ = 0.92, x₁=0.86, x40.94, x 0.95, x=0.73, xy = 0.90, X-0.49, x 0.79, *10= 0.79. (a) Use the method of moments to obtain an estimator of 1 O 0 (x-1)-2 0 (x-1)-1 O 0 (1+) -1 O -2 Compute the estimate for this data. (Round your answer to two decimal places.) (b) Obtain the maximum likelihood estimator of 0. Din(X)) n in(X) -n -n Din(x) n Ein(X) in(x) 1

Let X denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test. Suppose the pdf of Xis +1)x F(x; 6) = 0 otherwise where -1 <0. A random sample of ten students yields data x₁ = 0.65, x₂ = 0.92, x₁=0.86, x40.94, x 0.95, x=0.73, xy = 0.90, X-0.49, x 0.79, *10= 0.79. (a) Use the method of moments to obtain an estimator of 1 O 0 (x-1)-2 0 (x-1)-1 O 0 (1+) -1 O -2 Compute the estimate for this data. (Round your answer to two decimal places.) (b) Obtain the maximum likelihood estimator of 0. Din(X)) n in(X) -n -n Din(x) n Ein(X) in(x) 1

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...
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(b) Obtain the maximum likelihood estimator of 0. Ein(X) n Ein(X₂) -n -n Ein(x) n in(X) Ein(X) -1 n -1 Compute the estimate for the given data. (Round your answer to two decimal places.)
Transcribed Image Text:(b) Obtain the maximum likelihood estimator of 0. Ein(X) n Ein(X₂) -n -n Ein(x) n in(X) Ein(X) -1 n -1 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 Xis F(x; 6) = 0 otherwise where -1 <0. A random sample of ten students yields data x₁ = 0.65, x₂ = 0.92, x₁=0.86, x40.94, X-0.95, x=0.73, x=0.90, X-0.49, x 0.79, *10= 0.79. (a) Use the method of moments to obtain an estimator of 1 O 0 (x-1)-2 0 (x-1)-1 O 0 (1+)-1 -2 Compute the estimate for this data. (Round your answer to two decimal places.) (b) Obtain the maximum likelihood estimator of 0. Lin(X)) n Zn(x)) -n -n Din(x) n in(X) ΣΟΧ) 1
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 Xis F(x; 6) = 0 otherwise where -1 <0. A random sample of ten students yields data x₁ = 0.65, x₂ = 0.92, x₁=0.86, x40.94, X-0.95, x=0.73, x=0.90, X-0.49, x 0.79, *10= 0.79. (a) Use the method of moments to obtain an estimator of 1 O 0 (x-1)-2 0 (x-1)-1 O 0 (1+)-1 -2 Compute the estimate for this data. (Round your answer to two decimal places.) (b) Obtain the maximum likelihood estimator of 0. Lin(X)) n Zn(x)) -n -n Din(x) n in(X) ΣΟΧ) 1
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