Please help 11. Let P= 23be the transition matrix for a Markov chain. In the long-run, what is1/3the probability of being in state 1?a) 4/7b) 25c) 35d) 37e) none of the others

Name: Please help 11. Let P= 23be the transition matrix for a Markov chain.
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Please help 11. Let P= 23be the transition matrix for a Markov chain. In the long-run, what is1/3the probability of being in state 1?a) 4/7b) 25c) 35d) 37e) none of the others

Given: P=012/31/3 Substitute respective values in the equation Pπ=π. 012/31/3π1π2=π1π2Therefore from the above equation: π1=π223π1+13π2=π2π1+π2=1 since π1=π2, π1=π2=12. limn→∞P11n=π1=12 Therefore the probability of being in state 1 is 12. Hence the correct option is (e)