Q$2[20$ pt$]$ Exercise $5\mathrm{.}4$ of Alpaydin. For a two$-$class problem, for the four cases of Gaussian densities in table $5\mathrm{.}1,$ derive the expression of log $[$P$($C$1|$x$)/$ P$($C$2|$x$)]$ using $\backslash$Sigma i and $\backslash$mu i$,$ and simplify it as much as possible. There is no need to derive the condition for the boundary to be linear.