Consider a binary classification problem, where Y $=\{-1,+1\}.$ Assume a noisy scenario wherethe data is generated i$.$i$.$d$.$ from some P $($x$,$ y$).$ We have discussed in the class that when $0/1$ error function is considered, calculating the ideal mini$-$target on each x reveals the hidden target function of f$0/1($x$)=$ y belongs to $\{+1,1\}-$arg max P $($y $|$ x$)=$ sign$($P $(+1|$ x$)-1/2)$Instead of the $0/1$ error, if we consider the CIA error function, where a false positive $($classifying a negative example as a positive one$)$ is $1000$ times more important than a false negative, the hidden target should be changed to fCIA$($x$)=$ sign$($P $(+1|$ x$)-$ alpha $)$Prove what the value of alpha should be$.$