Consider the transition matrix:
$\begin{array} { l }
\left| \begin{array} { l l l }
.3 & .2&.5
\end{array} \right| \
\quad\quad\begin{array} { l l l }
\mid.1 & .6 & .3 \mid\
\mid .2 & .3 & .5\mid
\end{array} \
\end{array}$
The steady-state probability of being in state 1 is approximately:
A).177
B).231
C).300
D).403

Question

Consider the transition matrix:
$\begin{array} { l } 
\left| \begin{array} { l l l } 
.3 & .2&.5
\end{array} \right| \
\quad\quad\begin{array} { l l l } 
\mid.1 & .6 & .3 \mid\ 
\mid .2 & .3 & .5\mid 
\end{array} \
\end{array}$
The steady-state probability of being in state 1 is approximately:
A).177
B).231
C).300
D).403

Quizplus · Accepted Answer

The steady-state probability of being in state 1 is the first element of the eigenvector corresponding to the eigenvalue 1. The eigenvalue 1 is the largest eigenvalue of the transition matrix, and the corresponding eigenvector is the steady-state probability vector. The first element of the eigenvector is approximately 0.177.

Consider the Transition Matrix The Steady-State Probability of Being in State 1 Is Approximately