Consider a binary classification problem whereXRpandY {0,1}. For a fixedxRp, suppose that Pr(Y= 1|X=x) =pfor somep[0,1]. Consider a prediction problem where there is a lossLFN>0 associated with predictingY= 0 when the actual outcome isY= 1, and another lossLFP>0 associated with predictingY= 1 when the actual outcome isY= 0. There is no loss associated with true positives or true negatives (i.e., a correct answer). Show that there is a threshold valuep such that following the expected loss criterion for making a prediction is equivalent to predictingY= 1 ifpp and predictingY= 0 otherwise. What is the value ofp?