The one$-$dimensional class$-$conditional feature pdfs for a $2-$category classification problem have

triangular shapes: p$($x$|\backslash$omega $1)=1$ x$/2$ for $0<$ x $<2$ and zero elsewhere; p$($x$|\backslash$omega $2)=($x $1)/2$ for

$1<$ x $<3$ and zero elsewhere.

a$)$ Derive the Bayes classifier, assuming equal a priori probabilities.

b$)$ Find the location of the decision boundary