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approximately assume assumption ball Bayes rule calculations cells Chapter choose complete consider consists contains Continued convex course curve decision define Definition denote the event density derivative desired distribution easily easy elements equal equation essentially estimator Example exist expression fact Figure finite follows function given hence holds implies increases independent independent r.v.'s Inequality integer interesting interval involves least Lemma limit mean method minimal minimax normal Note obtain occurs otherwise P(AB possible probability Problem proof Random rejects replaced respect result risk point rule satisfy shown similar Similarly simple smallest solution sufficient statistic suppose Table Theorem tion true unbiased unique Var(x Variables yields zero ܘ ܘ ܘ