Let X₁, X₂ be independent random variables with mean and variance o, and a is a constant. We also know that μ = o. Suppose we have two estimators of μ: =1=1/(X₁ + X₂) 2 = X₁ + X₂ ) Calculate the bias of each estimator. ) What is the variance of each estimator? ) Calculate the relative efficiency of 2 with respect to 1. Determine the constant a such that μ2 ecomes a more efficient estimator.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Let X₁, X2 be independent random variables with mean μ and variance o2, and a is a constant.
We also know that μ = o. Suppose we have two estimators of μ:
P1 = (X₁ + X₂)
A₂ = X₁ + X₂
a) Calculate the bias of each estimator.
b) What is the variance of each estimator?
c) Calculate the relative efficiency of 2 with respect to ₁. Determine the constant a such that f
becomes a more efficient estimator.
Transcribed Image Text:Let X₁, X2 be independent random variables with mean μ and variance o2, and a is a constant. We also know that μ = o. Suppose we have two estimators of μ: P1 = (X₁ + X₂) A₂ = X₁ + X₂ a) Calculate the bias of each estimator. b) What is the variance of each estimator? c) Calculate the relative efficiency of 2 with respect to ₁. Determine the constant a such that f becomes a more efficient estimator.
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