Instructions: Please either typeset your answers $($LATEX recommended$)$ or write them very clearly

and legibly and scan them, and upload the PDF on edX. Legibility and clarity are critical for fair

grading.

$1.$ 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