Determine the long-run state of a transition model
An annual survey records the nesting site used by each tagged bird. Counts are represented by column state matrices
One application of the transition matrix represents one year. In \(S_n\), the index \(n\) counts the number of applications from \(S_0\)
Use the state order North site and River site. Each column of \(T\) is a current state and each row is the next state. The entries of each state matrix are counts of birds
\[T = \begin{bmatrix} 0.9 & 0.05 \\ 0.1 & 0.95 \end{bmatrix}\]
\[S_0 = \begin{bmatrix} 49 \\ 305 \end{bmatrix}\]
Use probe indices 10 and 34. Give probe counts to the nearest whole count