Consider a population with mean μ and variance σ2<∞. You are comparing two estimators ˆ μ 1 and ˆ μ 2 for the mean of the population μ, with the following expected values and variances E( ˆ μ 1)=μ;V( ˆ μ 1)=9; E( ˆ μ 1)=μ+1;V( ˆ μ 2)=1. We also know that the covariance between the two estimators is COV( ˆ μ 1, ˆ μ 2)=−2. Now consider a new estimator that combines the two previous ones ˆ μ 3= 1 3 ˆ μ 1+ 2 3 ˆ μ 2. Then the variance V( ˆ μ 3) of ˆ μ 3 is 单项选择题

A

σ2 -2

B

1.4444

C

σ2 + 1.4444

D

3.6667

E

2.7778

F

0.5556

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