Consider a Gaussian Naive Bayes classifier for a dataset with single attribute

$$

$$and

two classes

$0$

$$and

$1$

$.$

$$The parameters of the gaussian distributions are:

$$

$($

$$

$|$

$$

$=$

$0$

$)$

$$

$$

$($

$0$

$,$

$1$

$4$

$)$

$$

$($

$$

$|$

$$

$=$

$1$

$)$

$$

$$

$($

$0$

$,$

$1$

$2$

$)$

$$

$($

$$

$=$

$1$

$)$

$=$

$0$

$.$

$5$

Find the decision boundary for the classifier if the loss matrix is

$$

$=$

$[$

$0$

$2$

$1$

$0$

$]$

$.$