Astate vector x for a four-state markov chain is such that the system is four times as likely to be in state 2 as in 4, is not in state 3, and is in state 1 with probability 0.2. find the state vector. can someone tell me what the answer is ? i've literally tried this 40+ times and my homework says its wrong. it would be greatly appreciated.

All the components in the state vector need to sum to 1. You're given that component corresponding to state 1 is 0.2, and that the component for state 3 is 0.

That leaves states 2 and 4, for which you're told that the component for state 2 is four times as large. If is the component for state , then you have



which means . So the state vector is .