Question $2$: Using two$-$dimensional $(2$D$)$ features, design a linear Bayes classifier to distinguish between the two pattern classes modeled by the following given parameters of $2$D Gaussian distributions.

$\backslash$mu

$1$

$=[$

$3$

$2$

$],\backslash$mu

$2$

$=[$

$5$

$4$

$]$

$\backslash$Sigma

$1$

$=$

$[$

$0\mathrm{.}5$

$0$

$0$

$0\mathrm{.}5$

$]$

$,$

$\backslash$Sigma

$2$

$=$

$[$

$1$

$0$

$0$

$1$

$]$

$\backslash$Sigma

$1$

$=[$

$0\mathrm{.}5$

$0$

$0$

$0\mathrm{.}5$

$],\backslash$Sigma

$2$

$=[$

$1$

$0$

$0$

$1$

$]$

a$-$ Write the discriminant functions for Class $1$ and Class $2.$

b $-$ sing these functions, write the equation of the decision boundary that separates the decision regions of the two classes in the $2$D feature space.