Hi all,

The followings are the home work assignment that was 
given in the course on Monday 13th October.

The due date is ....  

We have calculated in the course that the boudary between 
two classes whose variance matrices and mean vector are

==================================
        0.10  0.00
Sigma =              ,mu = (0, 1)
        0.00  0.30
==================================
        0.20  0.00
Sigma =              ,mu = (1, 0)
        0.00  0.10
==================================

respectively, is a hyperbola:

==============================================
30 (x + 1)^2 - 40 (y + 0.5)^2 = 30 - 6 ln(3/2)
==============================================

and have also learned that the two classes:

==================================
        0.10  0.00
Sigma =              ,mu = (0, 1)
        0.00  0.30
==================================
        0.20  0.00
Sigma =              ,mu = (1, 0)
        0.00  0.10
==================================

give us a boundary of ellipsoid.

Then answer the following question.

(1) Obtain the equation of the above ellipsoid.
    not only the results but also the precedure
    to obtain the results.

(2) Give me two classes whose boundary is
    parabola. Variance matrix and mean vector
    for each of the two classes and the resultant 
    equation with its procedure are required.
    

(3) Same as (2) except for the boundary is circle

(4) Same as (2) except for the boundary is pair of lines