Consider a two$-$category classification problem in two dimensions. The CCPDFs are Ga$-$

ussians given by $p(x|w_1)N({}_1,{}_1)$ and $p(x|w_2)N({}_2,{}_2)$ where

${}_1=([0$

$0]),{}_1=([1,0$

$0,1])$

${}_2=([1$

$1]),{}_2=([1,0$

$0,1])$

$($a$)$ For equal prior probabilities, find the equation of the Bayes decision boundary, plot it$,$

and define the decision regions. MATLAB's Symbolic Toolbox might be helpful.

$($b$)$ Repeat part $($a$)$ if the prior probabilities are $P(w_1)=\frac{1}{4}$ and $P(w_2)=\frac{3}{4}.$

$($c$)$ Repeat parts $($a$)$ and $($b$)$ for the following:

${}_1=([0$

$0]),{}_1=([2,0\mathrm{.}5$

$0\mathrm{.}5,2])$

${}_2=([1$

$1]),{}_2=([5,4$

$4,5])$