You are given a transition matrix P. Find the steady-state distribution vector. $$P = \left[ \begin{array} { c c c }
0.3 & 0 & 0.7 \
1 & 0 & 0 \
0 & 0.6 & 0.4
\end{array} \right]$$
A)The steady-state distribution vector is $\left[ \frac { 11 } { 43 } \frac { 32 } { 43 } \quad \frac { 11 } { 43 } \right]$
B) The steady-state distribution vector is $\left[ \frac { 35 } { 86 } \quad \frac { 15 } { 43 } \frac { 21 } { 86 } \right]$
C) The steady-state distribution vector is $\left[ \begin{array} { l l l }
\frac { 15 } { 43 } & \frac { 21 } { 86 } & \frac { 35 } { 86 }
\end{array} \right]$
D) The steady-state distribution vector is $\left[ \frac { 25 } { 86 } \quad \frac { 13 } { 43 } \frac { 35 } { 86 } \right]$
E) The steady-state distribution vector is $\left[ \frac { 21 } { 86 } \quad \frac { 15 } { 43 } \frac { 35 } { 86 } \right]$

Question

You are given a transition matrix P. Find the steady-state distribution vector.   $$P = \left[ \begin{array} { c c c } 
0.3 & 0 & 0.7 \
1 & 0 & 0 \
0 & 0.6 & 0.4
\end{array} \right]$$  
A)The steady-state distribution vector is $\left[ \frac { 11 } { 43 } \frac { 32 } { 43 } \quad \frac { 11 } { 43 } \right]$
B) The steady-state distribution vector is $\left[ \frac { 35 } { 86 } \quad \frac { 15 } { 43 } \frac { 21 } { 86 } \right]$
C) The steady-state distribution vector is $\left[ \begin{array} { l l l } 
\frac { 15 } { 43 } & \frac { 21 } { 86 } & \frac { 35 } { 86 }
\end{array} \right]$
D) The steady-state distribution vector is $\left[ \frac { 25 } { 86 } \quad \frac { 13 } { 43 } \frac { 35 } { 86 } \right]$
E) The steady-state distribution vector is $\left[ \frac { 21 } { 86 } \quad \frac { 15 } { 43 } \frac { 35 } { 86 } \right]$

Quizplus · Accepted Answer

To find the steady-state distribution vector $\pi$ for a transition matrix $P$, we solve the equation $\pi P = \pi$ under the condition that the sum of the elements of $\pi$ equals 1. The correct steady-state distribution vector, given the transition matrix, is option C, which can be verified by ensuring that $\pi P = \pi$ and that the sum of the elements of $\pi$ equals 1.

You Are Given a Transition Matrix P P=[0.300.710000.60.4]P = \left[ \begin{array} { c c c } 0.3 & 0 & 0.7 \\1 & 0 & 0 \\0 & 0.6 & 0.4\end{array} \right]P=​0.310​000.6​0.700.4​​

You Are Given a Transition Matrix P $P = \left[ \begin{array} { c c c } 0.3 & 0 & 0.7 \\1 & 0 & 0 \\0 & 0.6 & 0.4\end{array} \right]$