Consider a population with mean 𝜇 and variance 𝜎 2 < ∞ . We collect an IID sample of 𝑇 = 3 observations. Assume the following estimators for the population mean: 𝜇 ̂ 1 = 2 3 𝑥 1 + 1 3 𝑥 2 + 1 3 𝑥 3 𝜇 ̂ 2 = 𝑥 1 + 2 𝑥 2 − 𝑥 3 . Now, consider another estimator 𝜇 ̂ 3 = 1 2 𝜇 ̂ 1 + 𝛼 𝜇 ̂ 2 . Which value of 𝛼 would make 𝜇 ̂ 3 unbiased for 𝜇 ? 单项选择题

A

1 3

B

0

C

1 6

D

1

E

1 2

F

2 3

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