Often in binary classification we are interested in the differences in the output of our current$$classifier$,$ g$,$ and an unknown function f that we are trying to learn. It is common in these$$cases to examine the quantity produced by f$($x$)$g$($x$)$ for a given input x$.$ For this problem,$$let D be an arbitrary distribution on the domain $\{1,1\}$n$,$ and let f$,$ g : $\{1,1\}$n $->\{1,1\}$be two Boolean functions.$($a$)[6$ points$]$ Prove that$$Px$$D$[$f$($x$)=$ g$($x$)]=1$ Ex$$D$[$f$($x$)$g$($x$)]2.$