Determine the long-run state of a transition model
A monthly record classifies each customer's subscription plan
One application of the transition matrix represents one month. In \(S_n\), the index \(n\) counts the number of applications from \(S_0\)
Use the state order Basic plan and Standard plan. Each column of \(T\) is a current state and each row is the next state. The entries of each state matrix are counts of customers
\[T = \begin{bmatrix} 0.9 & 0.05 \\ 0.1 & 0.95 \end{bmatrix}\]
\[S_0 = \begin{bmatrix} 206 \\ 34 \end{bmatrix}\]
Use probe indices 8 and 38. Give probe counts to the nearest whole count