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Algebra I: A Basic Course in Abstract Algebra by Rajendra Kumar Sharma, Sudesh Kumari Shah, Asha Gauri Shankar

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Chapter 18

Markov Process

Definitions and Examples

Suppose that each year 6% of the population of Delhi migrate to Mumbai and 4% of the population of Mumbai migrate to Delhi. Let the population of Delhi be x0 and that of Mumbai be y0. We are interested in knowing the population after 1, 2, 3 years.

Initial population vector X0 = [x0 y0]t if x1, y1 are the populations of Delhi and Mumbai after 1 year.

 

 

x1 = 0:94x0 + 0:04y0

 

y1 = 0:06x0 + 0:96y0

 

In the matrix form, we get

 

images

 

If X1 = [x1 y1]t is the population vector after 1 year

 

X1 = AX0

 

where

 

 

If X2 = [x2, y2]t is the population vector after 2 years, then we will get

 

X2 = AX ...

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