Section 9.1

(4)

S1 = S0P = [.3 .7]
 [
.8
.2
 ] = [(.3)(.8) + (.7)(.4) (.3)(.2) + (.7)(.6)] = [.52 .48]
 
.4
.6
  

(24)

   
A
B
C
  
A
[
0
1
0
 ]
B
.5
0
.5
C
1
0
0

(60)
(A) The following is the transition matrix P

   
H
R
  
H
[
.95
.05
 ]
R
.03
.97

(B) The initial state distribution matrix is S0 = [.733 .267]. After one decade (1990) the new state distribution matrix is
S1 = S0 P = [.733 .267]
 [
.95
.05
 ] = [.70436 .29564]
 
.03
.97
  
Thus about 70.4% of the households are home owners in 1990.

(C) After two decades (2000) the new state distribution matrix is

S2 = S1P = [.70436 .29564]
 [
.95
.05
 ] = [.6780112 .3219888]
 
.03
.97
  
Thus about 67.8% of the households are home owners in 2000.