If we want the expected number of time periods a chain is spent in state j given it started in state i, what are the steps for calculating this?

If we want the expected number of time periods a chain is spent in state j given it started in state i, what are the steps for calculating this?

• A. identify transient states and create PT matrix; 2) calculate the I - PT matrix; 3) calculate the S = 1 / (I-PT) matrix; 4) find Sij from S matrix
• B. compute stationary distribution; 2) multiply by initial state; 3) integrate; 4) read the row
• C. determine absorbing states; 2) compute Q; 3) compute N = (I - Q)^{-1}; 4) read N_ij
• D. form the full transition matrix P; 2) compute eigenvectors; 3) find fundamental matrix F = (I - P)^{-1}; 4) use F_ij

Answer: (A)