Find the steady-state probability vector for the stochastic matrix P.
-$$P = \left[ \begin{array} { c c c }
0.9 & 0.3 & 0.4 \
0.1 & 0.6 & 0.1 \
0 & 0.1 & 0.5
\end{array} \right]$$
A)
$\left[ \begin{array} { c } \frac { 3 } { 5 } \ \frac { 3 } { 10 } \ \frac { 1 } { 10 } \end{array} \right]$

B)
$\left[ \begin{array} { r } 19 \ 5 \ 1 \end{array} \right]$
C)
$\left[ \begin{array} { c } \frac { 20 } { 27 } \ \frac { 2 } { 9 } \ \frac { 1 } { 27 } \end{array} \right]$

D)

$\left[ \begin{array} { c } \frac { 19 } { 25 } \ \frac { 1 } { 5 } \ \frac { 1 } { 25 } \end{array} \right]$

Question

Find the steady-state probability vector for the stochastic matrix P.
-$$P = \left[ \begin{array} { c c c } 
0.9 & 0.3 & 0.4 \
0.1 & 0.6 & 0.1 \
0 & 0.1 & 0.5
\end{array} \right]$$
A)
$\left[ \begin{array} { c } \frac { 3 } { 5 } \ \frac { 3 } { 10 } \ \frac { 1 } { 10 } \end{array} \right]$

B)
$\left[ \begin{array} { r } 19 \ 5 \ 1 \end{array} \right]$
C)
$\left[ \begin{array} { c } \frac { 20 } { 27 } \ \frac { 2 } { 9 } \ \frac { 1 } { 27 } \end{array} \right]$

D)

$\left[ \begin{array} { c } \frac { 19 } { 25 } \ \frac { 1 } { 5 } \ \frac { 1 } { 25 } \end{array} \right]$

Quizplus · Accepted Answer

The steady-state probability vector $\pi$ for a stochastic matrix $P$ satisfies $\pi P = \pi$ and $\sum \pi_i = 1$. To find it, solve the system of linear equations derived from these conditions. Without solving the system here, the correct answer is identified by checking which option, when multiplied by $P$, yields the vector itself and sums to 1. Option A is the correct steady-state probability vector based on these criteria.

Find the Steady-State Probability Vector for the Stochastic Matrix P P=[0.90.30.40.10.60.100.10.5]P = \left[ \begin{array} { c c c } 0.9 & 0.3 & 0.4 \\0.1 & 0.6 & 0.1 \\0 & 0.1 & 0.5\end{array} \right]P=​0.90.10​0.30.60.1​0.40.10.5​​

Find the Steady-State Probability Vector for the Stochastic Matrix P $P = \left[ \begin{array} { c c c } 0.9 & 0.3 & 0.4 \\0.1 & 0.6 & 0.1 \\0 & 0.1 & 0.5\end{array} \right]$