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-i) \( (3\%) \) Find the posterior distribution of \( p \)