Determine the long-run state of a transition model
A weekly survey records which food outlet each student uses. Counts are represented by column state matrices
One application of the transition matrix represents one week. In \(S_n\), the index \(n\) counts the number of applications from \(S_0\)
Use the state order Main canteen and Sports kiosk. Each column of \(T\) is a current state and each row is the next state. The entries of each state matrix are counts of students
\[T = \begin{bmatrix} 0.6 & 0.3 \\ 0.4 & 0.7 \end{bmatrix}\]
\[S_0 = \begin{bmatrix} 53 \\ 437 \end{bmatrix}\]
Use probe indices 1 and 9. Give probe counts to the nearest whole count