You Are Given a Transition Matrix P $$P = \left[ \begin{array} { l l } \frac { 1 } { 5 } & \frac { 4 } { 5 } \\\frac { 1 } { 3 } & \frac { 2 } { 3 }\end{array} \right]$$

Multiple Choice

You are given a transition matrix P. Find the steady-state distribution vector. $$P = \left[ \begin{array} { l l } \frac { 1 } { 5 } & \frac { 4 } { 5 } \\\frac { 1 } { 3 } & \frac { 2 } { 3 }\end{array} \right]$$

A) The steady-state distribution vector is $\left[ \begin{array} { l l } \frac { 12 } { 17 } & \frac { 5 } { 17 }\end{array} \right]$
B) The steady-state distribution vector is $\left[ \begin{array} { l l } \frac { 1 } { 2 } & \frac { 1 } { 2 }\end{array} \right]$
C) The steady-state distribution vector is $\left[ \frac { 3 } { 13 } \frac { 10 } { 13 } \right]$
D) The steady-state distribution vector is $\left[ \frac { 5 } { 17 } \frac { 12 } { 17 } \right]$
E) The steady-state distribution vector is $\left[ \begin{array} { l l } \frac { 10 } { 13 } & \frac { 3 } { 13 }\end{array} \right]$