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Let x = ( x 1 , x 2 , 2 3 ) describe a patient's medical record, where each x in { 0 ,

Let x =(x1, x2,23) describe a patient's medical record, where each x in {0,1}.(For example, each x could record the binary outcome of a certain lab test). The label y indicates the presence or absence of a certain disease, with y in {0,1}. Suppose the prior distribution of Y is P(Y =0)=0.8, and P(Y =1)=0.2, and the likelihood is P(X=(x1, x2, x3)|Y = y)=3-1(0.5+0.25)(0.75-0.5)1-2. If h is the predicted outcome while the truth is y, the loss l(h, y) incurred is given by l(0,0)=0, l(0,1)=+1000, l(1,0)=+100, and (1,1)=-500.(i) Determine the Bayes Optimal hypothesis h Bayes-Optimal.
(ii) What is the Bayes Optimal Risk?

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