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\noindent
{\it Pattern recognition} (CSE-586)  12 June 2001\\
\noindent
Name [ \hspace{2in} ] \hspace{.1in} Student-ID [ \hspace{1in} ]\\

\noindent
\begin{itemize}
\item[1.] Obtain boundary
when $p(\omega_1)=p(\omega_2)$, $\mu_1=(0, 0)$, $\mu_2=(1, 1)$,\mbox{ and}
$
\Sigma_1 = \Sigma_2 =
\left(
\begin{array}{cc}
0.1 & 0             \\
0   & 0.1
\end{array}
\right).
$
\vspace{4in}
\item[2.] Obtain boundary
when $p(\omega_1)=p(\omega_2)$, $\mu_1=(0, 1)$, $\mu_2=(1, 0)$,
$
\Sigma_1 =
\left(
\begin{array}{cc}
0.1 & 0             \\
0   & 0.3
\end{array}
\right),\mbox{and} \hspace{.1in}
\Sigma_2 =
\left(
\begin{array}{cc}
0.2 & 0             \\
0   & 0.1
\end{array}
\right).
$
\clearpage
\item[3.] Clasify $\mbox{\bf x}=(5/2, 5/2)$ with the Bayesian classifier 
when we have two classes $\omega_1$ and $\omega_2$
where $p(\omega_1)=p(\omega_2)$, $\mu_1=(0, 0)$, $\mu_2=(5, 5)$, and
$
\Sigma_1 = \Sigma_2 = 
\left(
\begin{array}{cc}
1.2 & 0.4             \\
0.4 & 1.8
\end{array}
\right).
$
\vspace{6in}
\item[4.] 
When the samples from $\omega_1$ are $(3, 6)$, $(5, 5)$ and $(7, 7)$
and the samples from $\omega_2$ are $(6, 8)$, $(6, 7)$ and $(8, 5)$,
clasify $\mbox{\bf x}=(6, 6)$ in the following two algorithms 
under the Eucledian distance with describing the reason breifly.
   \begin{itemize}
   \item[(1)] Nearest Neighbor Algorithm (NN)
   \item[]
   \item[]
   \item[]
   \item[]
   \item[]
   \item[(1)] 3NN
   \end{itemize}
\end{itemize}
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