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Question: What are the steady state probabilities of the transition matrix: |0.90 0.10| |0.70 0.30| A...

Question: What are the steady state probabilities of the transition matrix: |0.90 0.10| |0.70 0.30|
A [0.33 0.67]
B [0.50 0.50]
C [0.25 0.75]
D [0.88 0.12]
Math   Statistics-And-Probability   
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Answer #1

The equilibrium chance for any particular state, also called as the steady state probabilities, are obtained by solving for the equation

The logic behind this is that the steady state probabilities should remain unaltered, if it is multiplied by the transition matrix, since this multiplication denotes the state probabilities for the next day. Hence, we obtain

Even by opening the product along the other column, we shall get the same equation. The other conbdition here is the normalization of probabilities, viz. the sum of probabilities of all states must be zero. Hence,

Solving these two equations, we obtain the steady state probabilities,

Hence, option D is correct by rounding off

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