題組內容

3. (30%) Let X₁, X₂, ..., Xₙ be a random sample from Bernoulli(p). Define R(p, δ(X)) = Eₚ[(δ(X) - p)²] (the Mean-Square Error).
(c) Assume that the prior distribution on \( p \) is beta \( (\alpha, \beta) \).

(c-iii) \( (3\%) \) Denote \( \hat{p}B \) to be the posterior mean found in (c-ii). Find \( \alpha, \beta \) such that \( R(p, \hat{p}B) \) is constant.

阿摩線上測驗 · 2026-10-22T10:31:50+08:00

(c-iii) (3%) Denote pB to be the posterior mean found in (c-ii). Find α, β such that R(p, pB) is constant.

題組內容

(c-iii) \( (3\%) \) Denote \( \hat{p}B \) to be the posterior mean found in (c-ii). Find \( \alpha, \beta \) such that \( R(p, \hat{p}B) \) is constant.

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