Suppose that X1, X2 are two independent random variables with a common mean μ, but two...

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Suppose that X1, X2 are two independent random variables with a common mean μ, but two...

Suppose that X₁, X₂ are two independent random variables with a common mean μ, but two different variances σ₁² > σ₂². Consider the family of estimators

W_α = αX₁ + (1−α)X₂

where 0 ≤ α ≤ 1

(a) Show that W_α is an unbiased estimator of μ for any value of α.

(b) Find the value of α which makes W_α as efficient as possible. Explain why the resulting formula makes sense.

math Statistics-And-Probability

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