Suppose there is an epidemic in which every month half of those who are well become sick, half of those who are sick get well, and a quarter of those who are sick die. Find the steady state for the corresponding Markov process

\[

\left(\begin{array}{l}

w_{n+1} \\

s_{n+1} \\

d_{n+1}

\end{array}\right)=\left(\begin{array}{ccc}

\frac{1}{2} & \frac{1}{2} & 0 \\

\frac{1}{2} & \frac{1}{4} & 0 \\

0 & \frac{1}{4} & 1

\end{array}\right)\left(\begin{array}{l}

w_{n} \\

s_{n} \\

d_{n}

\end{array}\right)

\]