![\mathbf{P_2 = \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}](/tpl/images/0682/6194/cb6b9.png)
![= \left[\begin{array}{c}140 \\ 160 \\ 200 \end{array}\right]}](/tpl/images/0682/6194/6b891.png)
![M = \left[\begin{array}{ccc} \dfrac{1}{5} & \dfrac{2}{5} &\dfrac{1}{5} \\ \\ \dfrac{2}{5}&\dfrac{2}{5}&\dfrac{1}{5}\\ \\ \dfrac{2}{5}& \dfrac{2}{5}& \dfrac{2}{5} \end{array}\right]](/tpl/images/0682/6194/aaa12.png)
![P = \left[\begin{array}{c}130 \\ 300 \\ 70 \end{array}\right]](/tpl/images/0682/6194/0bba9.png)
![P_2 = [M]^2 [P]](/tpl/images/0682/6194/cec3b.png)
![[M]^ 2 = \left[\begin{array}{ccc} \dfrac{1}{5} & \dfrac{2}{5} &\dfrac{1}{5} \\ \\ \dfrac{2}{5}&\dfrac{2}{5}&\dfrac{1}{5}\\ \\ \dfrac{2}{5}& \dfrac{2}{5}& \dfrac{2}{5} \end{array}\right] \left[\begin{array}{ccc} \dfrac{1}{5} & \dfrac{2}{5} &\dfrac{1}{5} \\ \\ \dfrac{2}{5}&\dfrac{2}{5}&\dfrac{1}{5}\\ \\ \dfrac{2}{5}& \dfrac{2}{5}& \dfrac{2}{5} \end{array}\right]](/tpl/images/0682/6194/3bc9b.png)
![[M]^ 2 = \dfrac{1}{25} \left[\begin{array}{ccc} 1+2+4 & 1+2+4 &1+2+4 \\ \\ 2+2+4&2+2+4&2+2+4\\ \\ 2+4+4&2+4+4& 2+4+4 \end{array}\right]](/tpl/images/0682/6194/e68ee.png)
![[M]^ 2 = \dfrac{1}{25} \left[\begin{array}{ccc}7&7&7 \\ \\ 8 &8&8\\ \\10&10& 10 \end{array}\right]](/tpl/images/0682/6194/8b4fd.png)
![P_2 = \dfrac{1}{25} \left[\begin{array}{ccc}7&7&7 \\ \\ 8 &8&8\\ \\10&10& 10 \end{array}\right] \left[\begin{array}{c}130 \\ 300 \\ 70 \end{array}\right]](/tpl/images/0682/6194/2892d.png)
![P_n = [M]^n [P]](/tpl/images/0682/6194/83345.png)
![[M]^n \ can \ be \ [M]^2 , [M]^3 , [M]^4 .... \infty](/tpl/images/0682/6194/07262.png)
![[M]^2 , [M]^3 , [M]^4 .... \infty](/tpl/images/0682/6194/19e1d.png)
we will always result to the value for ![[M]^n](/tpl/images/0682/6194/c2867.png)
; Now if 2/5 2/5 1/5
Mathematics, 11.06.2020 03:57 9tpompey
The following is a Markov (migration) matrix for three locations
[1/5 1/5 2/5
2/5 2/5 1/5
2/5 2/5 2/5]
(a) Initially, there are 130 individuals in location 1, 300 in location 2, and 70 in location 3. How many are in each location after two time periods?
(b) The total number of individuals in the migration process is 500. After a long time, how many are in each location?
Answers: 2
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You know the right answer?
The following is a Markov (migration) matrix for three locations
[1/5 1/5 2/5
2/5 2/5 1/5
2/5 2/5 1/5
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