115年
第 4 題20 分
本題為申論/計算題;請先作答,再依非官方 worked solution 與步驟 rubric 自評。查看原始試卷
Let Y₁, Y₂, and Y₃ be an independent and identically distributed random sample from a distribution with mean μ and variance σ² < ∞. Consider the following estimators for μ: m₁ = Y₁, m₂ = (Y₁ + αY₂) / (1 + α), m₃ = (Y₁ + 2Y₂ + βY₃) / (1 + 2 + β), where α > 0 and β > 0. (A). Determine which of the estimators m₁, m₂, and m₃ are unbiased for μ? (10%) (B). Find the value of α that minimize Var(m₂). (5%) (C). Find the value of β that minimize Var(m₃). (5%)
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