Let x $=($x$1,$ x$2,23)$ 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 YisP$($Y $=0)=0\mathrm{.}8,$ and P$($Y $=1)=0\mathrm{.}2,$ and the likelihood is P$($X$=(*1,*2,*3)|$Y$=$y$)=$ II $*3*1(0\mathrm{.}5+0\mathrm{.}25)(0\mathrm{.}75*0\mathrm{.}5)*1*2.$ If h is the predicted outcome while the truth is y$,$ the loss l$($h$,$ y$)$ incurred is given by l $(0,0)=0,1(0,1)=1000,$ I$(1,0)=100$ and l$(1,1)=500.($i$)$ Determine the Bayes Optimal hypothesis h Bayes $-$ Optimal. $($ii$)$ What is the Bayes Optimal Risk?