\documentstyle[12pt,eclepsf]{article}

\textheight 260mm
\topmargin -10mm
\textwidth 180mm
\oddsidemargin -7mm
\pagestyle{empty}

\begin{document}
\thispagestyle{empty}
\noindent
{\it The Final-exam of the Basic Course of Neural Networks (26 Jan 2001)}\\

The intermediate parameters are as follows:

\begin{eqnarray}
\nonumber
h^1_1 &=& h^1_2 = 0.5 \times 1.0 + 0.5 \times 1.0 + 0.5 \times 1.0 = 1.5 \\
\nonumber
y^1_1 &=& y^1_2 = 0.3 \times 1.5 = 0.45 \\
\nonumber
h^2_1 &=& 0.45 \times 0.5 +  0.45 \times 0.5 = 0.45 \\
\nonumber
y^2_1 &=& 0.3 \times 0.45 = 0.135 \\
\nonumber
\hat y_1  &=& (1.0+1.0+1.0)/5 = 0.6 \\
\nonumber
e_1 &=& 0.135 - 0.6 = -0.465 \\
\nonumber
\delta _1^2 &=& -0.465 \times 0.3 = -0.1395\\
\nonumber
e^1_1 &=& e^1_2 = -0.1385 \times 0.5 = -0.96975\\
\nonumber
\delta _1^1 &=& \delta _2^1 = -0.06975 \times 0.3 = -0.020925 \\
\nonumber
\end{eqnarray}
So, amounts of weight modification are:
\begin{eqnarray}
\nonumber
\triangle w^1_{11} &=& -0.1 \cdot \delta^1_1 \cdot y^0_1=-0.1 \times
   (-0.020925) \times 1.0 = 0.0020925 \\
\nonumber
\triangle w^1_{12} &=& -0.1 \cdot \delta^1_1 \cdot y^0_2= 0.0020925 \\
\nonumber
\triangle w^1_{13} &=& -0.1 \cdot \delta^1_1 \cdot y^0_3= 0.0020925 \\
\nonumber
\triangle w^1_{21} &=& -0.1 \cdot \delta^1_2 \cdot y^0_1= 0.0020925 \\
\nonumber
\triangle w^1_{22} &=& -0.1 \cdot \delta^1_2 \cdot y^0_2= 0.0020925 \\
\nonumber
\triangle w^1_{23} &=& -0.1 \cdot \delta^1_2 \cdot y^0_3= 0.0020925 \\
\nonumber
\triangle w^2_{11} &=& -0.1 \cdot \delta^2_1 \cdot y^1_1=-0.1 \times
   (-0.1395) \times 0.45 = 0.0062775 \\
\nonumber
\triangle w^2_{12} &=& -0.1 \cdot \delta^2_1 \cdot y^1_2 = 0.0062775 \\
\end{eqnarray}

\noindent
Hence,the answers should be:
\begin{displaymath}
\begin{array}{lllll}
w^1_{11}=  0.5020925 & w^1_{12}= 0.5020925 & 
w^1_{21}=  0.5020925 & w^1_{22}= 0.5020925 & \\
w^1_{31}=  0.5020925 & w^1_{32}= 0.5020925 & 
w^2_{11}=  0.5062775 & w^2_{12}= 0.5062775 &
\end{array}
\end{displaymath}
\hspace{.1in}\\
\noindent
Note that when your eight weight values are all correct your mark is 100,
otherwise you get 10 for each correct answer for the bellow.
\begin{displaymath}
\begin{array}{lllll}
h^1_2(1)= 1.5  & y^1_1(1)= 0.45 & y^2_1(1)= 0.135  & 
\hat y^2_1(1)= 0.6 & e_1(1)= -0.465\\
e^1_1(1)= -0.06975 &{\delta}^2_1(1)= -0.1395 & 
{\delta}^1_1(1)= -0.020925 &\triangle w^1_{12}=0.0020925  & 
w^1_{12}=0.5090925
\end{array}
\end{displaymath}

\end{document}