Consider a simple binary classification problem with $1-$dimensional inputs and re$-$

sponses being $+1,-1.$ Suppose that we are given $9$ training data points shown in

the following figure:

Answer the following questions.

$($a$)$ We can use the $1-$nearest neighbor classifier to predict the label of an arbitrary

test data input x$\_($test $).$ Mark on the axis of real numbers all such x$\_($test $)$ in the

interval $0,6$ for which the prediction is y$\_($pred $)=+1.$

$[4$ marks$]$

$($b$)$ We can also use the $7-$nearest neighbor classifier to predict the label of x$\_($test $).$

Mark on the axis of real numbers all such x$\_($test $)$ in the interval $0,6$ for which

the prediction is y$\_($pred $)=+1.$

$[4$ marks$]$

$($c$)$ For k$=1,3,5,7,9,$ denote by f$\_($k$)($x$)$ the k$-$nearest neighbour classifier given

by the $9$ training data points. For which value$($s$)$ of k is x$=2$ on the decision

boundary of f$\_($k$)($x$)?$

$[6$ marks$]$

$[$Total: $14$ marks$]$