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

Multiple Choice

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 $\left[ \begin{array} { l l l } \frac { 1 } { 3 } & \frac { 1 } { 3 } & \frac { 1 } { 3 }\end{array} \right]$