If any one can help, I have no clue how to solve this problem: In a study, the v
ID: 3060236 • Letter: I
Question
If any one can help, I have no clue how to solve this problem: In a study, the various stages of sleep for a large group of people were monitored in 30-second intervals, or "epochs." For each epoch, sleep stage was categorized as Wake, REM, or Non-REM. The accompanying table provides a summary of the results. Each cell of the table gives the number of epochs that occurred when transitioning from the previous sleep stage to the current sleep stage. Complete parts a through e below.
Sleep stage data table
Current Stage Non-REM REM Wake
Non-REM 31,111 152 1,768
REM 344 7,093 154
Wake 1,541 368 6,330
Totals 32,996 7,613 8,252
Any help appreciate. I am unsure of how to solve. Thank you!
Explanation / Answer
The matrix van be converted to transition probability matrix where P(i,j) that is from state i to state j Pij=Nij/Sum(Nij) for j=1,2,3 which is the number transitioned from state i to j divided by the sum of row i.
For example P(NonREM, NonRem)=31111/(31111+152+1768), P(REM,NonRem)=344/(344+7093+154) P(Wake,NonRem)=1541/(1541+368+6330) and similarly P(Nonrem,Rem), P(NonRem,Wake), P(Rem,Rem), P(Rem,Wake), P(wake,Rem) and P(Wake,Wake) can be calculated.
Once we get the probability matrix A. then the steady state probabilities can be found as given the initial state s b, the steady state is lim(n tends to infinity){A^n*b}