Problem 1184

Sir SagarDecember 11, 20150

Find the absorbing state(s) for the transition matrix shown.

$\begin{bmatrix} 1.0 & 0.00 &0.00 \\ 1.0&0.0 & 0.0\\ 0.3& 0.7 & 0.0 \end{bmatrix}$

Solution:-

A state is an absorbing state of a Markov chain if P_ii=1. Thus, check the entries P_11,P_22,and P₃₃to see if any of them are equal to 1.

P₁₁ = 1.1

P₂₂ = 0.0

P₃₃ = 0.0

Since P₁₁ equals 1, state 1 is the absorbing state.

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