We have seen that in p=2 dimensions, a linear decision boundary takes the form \\\\beta \ 0\ \ +\\\\beta \ 1\ \ X \ 1\ \ +\\\\beta \ 2\ \ X \ 2\ \ =0. We now investigate a non-linear decision boundary. (a) Sketch the curve (1+X \ 1\ \ ) \ 2\ +(2X \ 2\ \ ) \ 2\ =4 and (1+X \ 1\ \ ) \ 2\ +(2X \ 2\ \ ) \ 2\ =16 (b) On your sketch, indicate the set of points for which \ (1+X \ 1\ \ ) \ 2\ +(2X \ 2\ \ ) \ 2\ >16,\ 16>=(1+X \ 1\ \ ) \ 2\ +(2X \ 2\ \ ) \ 2\ >=4,\ \ as well as the set of points for which (1+X \ 1\ \ ) \ 2\ +(2X \ 2\ \ ) \ 2\ <4 c) suppose that a classifier assigns an observation to the blue if 16style="">=(1+X \ 1\ \ ) \ 2\ +(2X \ 2\ \ ) \ 2\ >=4 and to the red class otherwise. To what class is the observation (0,0) classified? (1,1)?(2,2)?(3,4)? d) Argue that while the decision boundary in (c) is not linear in terms of X \ 1\ \ and X \ 2\ \ , it is linear in terms of X \ 1\ \ ,X \ 1\ 2\ \ ,X \ 2\ \ , and X \ 2\ 2\ \ .