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Let x1, X2, ..., Xn be a random sample from a continuous uniform distribution with domain (0,b). This means that f(x) = 1/b for 0

Let x1, X2, ..., Xn be a random sample from a continuous uniform distribution with domain (0,b). This means that f(x) = 1/b for 0

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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10 Let x1, X2, Xn be a random sample from a continuous uniform distribution with domain (0,b). This means that f(x) = 1/b for 0 .... < x < b. Is 2*x-bar an unbiased estimator for b? For the instructor, this was question 4. / Yes, because E(X) = (1/2)*b, so E(X-bar) = (1/2)*b, so E(2*X-bar) = b. X Yes, because 2*x-bar is the method of moments estimator for b. X No, because the sample mean would be an unbiased estimator, not 2 times that value. X No, because 2*x-bar could give you a value smaller that the largest data point. X It depends on the sample size (how large n is). %3D
Transcribed Image Text:10 Let x1, X2, Xn be a random sample from a continuous uniform distribution with domain (0,b). This means that f(x) = 1/b for 0 .... < x < b. Is 2*x-bar an unbiased estimator for b? For the instructor, this was question 4. / Yes, because E(X) = (1/2)*b, so E(X-bar) = (1/2)*b, so E(2*X-bar) = b. X Yes, because 2*x-bar is the method of moments estimator for b. X No, because the sample mean would be an unbiased estimator, not 2 times that value. X No, because 2*x-bar could give you a value smaller that the largest data point. X It depends on the sample size (how large n is). %3D
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