8 = 1/2 ( 12 x₁ + ² x₂ + 2 x ₂ + ² x ₁ + ... + — Y+7 Y₁0) 10 Is this estimator unbiased? Compare the variance of this estimator to the variance of the usual Y estimator.

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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As we know, Ỹ is not the only estimator for the population mean. Consider the following alternative
estimator for the population mean (assuming iid sampling from distribution with mean equal to μy
and variance equal to o.):
Y = 1/2 ( ² X ₁ + ² X ₂ +
10 4
1 2 + — X₁ + ² X ₁ + ... + —- X₂ + ²—7 X₁0 )
² X ²
x
Is this estimator unbiased?
Compare the variance of this estimator to the variance of the usual Ỹ estimator.
Transcribed Image Text:As we know, Ỹ is not the only estimator for the population mean. Consider the following alternative estimator for the population mean (assuming iid sampling from distribution with mean equal to μy and variance equal to o.): Y = 1/2 ( ² X ₁ + ² X ₂ + 10 4 1 2 + — X₁ + ² X ₁ + ... + —- X₂ + ²—7 X₁0 ) ² X ² x Is this estimator unbiased? Compare the variance of this estimator to the variance of the usual Ỹ estimator.
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