想要请教大家下面这道题目: Use the binomial model for X with n=25; 0<θ<1, A={a1,a2} where a1 means:“ say θ<=0.2”and a2 means:”say θ>0.2”. a)Let the loss be L(a1,θ)= 0, ifθ<=0.2 or 5, ifθ>0.2 L(a2,θ)= 10, ifθ<=0.2 or 0, ifθ>0.2 Find the Bayes procedure for a Beta prior with α=6 and β=18 b)Consider the following class of decision procedures: t(x)=a2 if and only if X>C where C can be any value in {0,1,2,…,n-1} Find C such that the defined procedure is a frequentist test of size α=0.05 c)Show that there is a Beta prior such that the corresponding Bayes procedure is the frequentist test in (b). d)Assume the prior is Uniform on the interval 0 to 1. Show that there is a very drastic modification of the loss function above which makes the frequentist test in (b) a Bayes procedure wrt this prior. 下面是我现在遇到困难的地方~ a)我有解出到 Bayes Procedure t(x)=a1 iff 1/3<=P(θ<=0.2|x) a2 otherwise 不知道要如何把x解出来 b)从这条式子P(X>C|θ=0.2)<=0.05有解出C=8 不知道对不对 c)是指说改变Beta(α,β)中的α和β让Bayes procedure 变成 frequentist test吗? d)就完全没有头绪了 可以请大家给点想法吗? 谢谢大家^^ --

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