Transition Probability Matrix For Markov Chain Analysis
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the population of a city = 100000 Two Milk providing Company 1 Sun City CompanyGain 2 Suburb Company Loss
Loss Gain
Sun City Suburb 0.65 0.45 0.35 0.55
Transition Propability Matrix 1 Current Year
Dr. Sangita
First Year Population after first(one) year
2 Second Year
Population after Second(two) year
3 Third Year
Population after thirdt(three) year
4 ……..Year
Population after …………. year
5 ……..Year
Population after …………. year
0.65 0.35 0.58 0.42 100000
0.65 0.35 0.57 0.43 100000
0.65 0.35 0.56 0.44 100000
0.65 0.35 0.56 0.44 100000
0.65 0.35
0.45 0.55
X
0.65 0.35
X
0.58 0.42
X
0.57 0.43
X
0.56 0.44
X
0.56 0.44
58000 42000 100000 0.45 0.55
56600 43400 100000 0.45 0.55
56320 43680 100000 0.45 0.55
56264 43736 100000 0.45 0.55
0.56 0.44 100000 56252.8 43747.2 100000
6 ……..Year
Population after …………. year
7 ……..Year
Population after …………. year
8 ……..Year
Population after …………. year
Steady State Vector or Stable Vector or Equillibrium Vector
9 ……..Year
(same value of vector multiple) Population after …………. year
10 ……..Year
Population after …………. year
Direct Computation of Steady State Vector
0.65 0.35 0.56 0.44 100000
0.65 0.35 0.56 0.44 100000
0.65 0.35 0.56 0.44 100000
0.65 0.35 0.56 0.44 100000
0.65 0.35 0.56 0.44 100000
0.45 0.55
X
0.56 0.44
X
0.56 0.44
X
0.56 0.44
X
0.56 0.44
X
0.56 0.44
### ### 100000 0.45 0.55
### ### 100000 0.45 0.55
### ### 100000 0.45 0.55
56250 43750 100000 0.45 0.55
56250 43750 100000
0.65 0.35
0.45 0.55
0.65
0.45
-
Index matrix 1 0
To conver this matrix as Index matreix R1=R1 1 0 R2=R2+R1 0 1
0.35
0.55
-0.35 0.35
0.45 -0.45
-0.35 0
0.45 0
Index matrix 0 1
Loss Gain
Sun City Suburb 0.65 0.45 0.35 0.55
Transition Propability Matrix 1 Current Year
Dr. Sangita
First Year Population after first(one) year
2 Second Year
Population after Second(two) year
3 Third Year
Population after thirdt(three) year
4 ……..Year
Population after …………. year
5 ……..Year
Population after …………. year
0.65 0.35 0.58 0.42 100000
0.65 0.35 0.57 0.43 100000
0.65 0.35 0.56 0.44 100000
0.65 0.35 0.56 0.44 100000
0.65 0.35
0.45 0.55
X
0.65 0.35
X
0.58 0.42
X
0.57 0.43
X
0.56 0.44
X
0.56 0.44
58000 42000 100000 0.45 0.55
56600 43400 100000 0.45 0.55
56320 43680 100000 0.45 0.55
56264 43736 100000 0.45 0.55
0.56 0.44 100000 56252.8 43747.2 100000
6 ……..Year
Population after …………. year
7 ……..Year
Population after …………. year
8 ……..Year
Population after …………. year
Steady State Vector or Stable Vector or Equillibrium Vector
9 ……..Year
(same value of vector multiple) Population after …………. year
10 ……..Year
Population after …………. year
Direct Computation of Steady State Vector
0.65 0.35 0.56 0.44 100000
0.65 0.35 0.56 0.44 100000
0.65 0.35 0.56 0.44 100000
0.65 0.35 0.56 0.44 100000
0.65 0.35 0.56 0.44 100000
0.45 0.55
X
0.56 0.44
X
0.56 0.44
X
0.56 0.44
X
0.56 0.44
X
0.56 0.44
### ### 100000 0.45 0.55
### ### 100000 0.45 0.55
### ### 100000 0.45 0.55
56250 43750 100000 0.45 0.55
56250 43750 100000
0.65 0.35
0.45 0.55
0.65
0.45
-
Index matrix 1 0
To conver this matrix as Index matreix R1=R1 1 0 R2=R2+R1 0 1
0.35
0.55
-0.35 0.35
0.45 -0.45
-0.35 0
0.45 0
Index matrix 0 1
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