You are given a transition matrix P. Find the steady-state distribution vector. $$P = \left[ \begin{array} { c c c }
\frac { 2 } { 3 } & \frac { 1 } { 3 } & 0 \
\frac { 2 } { 3 } & \frac { 1 } { 3 } & 0 \
\frac { 2 } { 3 } & 0 & \frac { 1 } { 3 }
\end{array} \right]$$
A)The steady-state distribution vector is $\left[ \begin{array} { l l l }
0 & 0 & 1
\end{array} \right]$
B) The steady-state distribution vector is $\left[ \begin{array} { l l l }
\frac { 2 } { 3 } & 0 & \frac { 1 } { 3 }
\end{array} \right]$
C) The steady-state distribution vector is $\left[ \begin{array} { l l l }
\frac { 2 } { 3 } & \frac { 1 } { 3 } & 0
\end{array} \right]$
D) The steady-state distribution vector is $\left[ \begin{array} { l l l }
0 & \frac { 1 } { 3 } & \frac { 2 } { 3 }
\end{array} \right]$
E) The steady-state distribution vector is $\left[ \begin{array} { l l l }
\frac { 1 } { 3 } & \frac { 1 } { 3 } & \frac { 1 } { 3 }
\end{array} \right]$

Question

You are given a transition matrix  P. Find the steady-state distribution vector.   $$P = \left[ \begin{array} { c c c } 
\frac { 2 } { 3 } & \frac { 1 } { 3 } & 0 \
\frac { 2 } { 3 } & \frac { 1 } { 3 } & 0 \
\frac { 2 } { 3 } & 0 & \frac { 1 } { 3 }
\end{array} \right]$$  
A)The steady-state distribution vector is $\left[ \begin{array} { l l l } 
0 & 0 & 1
\end{array} \right]$
B) The steady-state distribution vector is $\left[ \begin{array} { l l l } 
\frac { 2 } { 3 } & 0 & \frac { 1 } { 3 }
\end{array} \right]$
C) The steady-state distribution vector is $\left[ \begin{array} { l l l } 
\frac { 2 } { 3 } & \frac { 1 } { 3 } & 0
\end{array} \right]$
D) The steady-state distribution vector is $\left[ \begin{array} { l l l } 
0 & \frac { 1 } { 3 } & \frac { 2 } { 3 }
\end{array} \right]$
E) The steady-state distribution vector is $\left[ \begin{array} { l l l } 
 \frac { 1 } { 3 }  & \frac { 1 } { 3 } & \frac { 1 } { 3 }
\end{array} \right]$

Quizplus · Accepted Answer

The steady-state distribution vector is the eigenvector of the transition matrix corresponding to the eigenvalue 1. The eigenvalue of the given matrix is 1 and the corresponding eigenvector is $\left[ \begin{array} { l l l } \frac { 2 } { 3 } & \frac { 1 } { 3 } & 0\end{array} \right]$.

You Are Given a Transition Matrix P A)The Steady-State Distribution Vector Is