114年
第 5 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, ..., Yₜ be an identical and independent sample from population Ω with mean μ and variance σ². T is a multiple of 5. Define estimator m as: m = [Σᵀᵢ₌₁ g(i)Yᵢ] / [Σᵀᵢ₌₁ g(i)], where g(i) = 1 + (i mod 5) and mod is the modular operator. (1) Prove that m is an unbiased estimator for μ. (10%) (2) What is the variance of m? (10%)
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