University of Illinois
College of Business Administration
Department of Information & Decision Sciences
IDS 594 (Special Topics in IDS) Statistical Finite
Mixture Models -- Classification and Cluster Analysis
Fall Semester, 2002
Prof. Stanley L. Sclove
Homework B Due Tuesday,
12-November-2002
Classification
1. The K = 3 class-conditional
densities are exponential with
means m =
10, 20 and 30.
(The mean is 1/l,
where l is the natural parameter.)
(a)
If there are equal prior probabilities and x = 20,
find the probability that x came from the population with
mean
equal to 20.
(b) Find the three classification regions, Rk
= {x: Say Pk}, k
= 1,2,3..
Model-Selection for Histograms
2. For the
days ill dataset, use SIC to compare three histograms, one with bins
0, 1, 2, . . . , 18, a second with bins (0),(1,2),(3,4), . . . , (17, 18),
and a third with bins (0),(1,2,3),(4,5,6),(7,8,9),(10,11,12),(13,14,15),(16,17,18).
K-Means Cluster Analysis
3. Do a K-Means clustering of the crude
oil prices , using a number of clusters and starting points suggested
by the histograms from Homework A. (Use Minitab or other software.)
Copyright (C) 2002 Stanley Louis Sclove
created 2002: May 29
latest revision 2002: Oct 31