Need help with Markov's Chain

Question

A state vector X for a four-state Markov chain is such that the system is four times as likely to be in state 3 as in 2, is not in state 4, and is in state 1 with probability 0.2. Find the state vector X.

Answer 1

Hi Morgan M.,

I'd guess that "state vector" is a fancy term for the probability "vector" that the system is in the respective states. Since P(4)=0, and P(1)=0.2, then P(2 or 3)=0.8. So let x=P(2), then P(3)=4x, and 5x=0.8, so x = 0.16. So P(3) = 4*0.16 = 0.64, and the "state vector X" = (0.2, 0.16, 0.64, 0) . This is just simple algebra, right? But you'll be getting to Markov chains presently, in which you may trace a "state vector" through successive operations (changes of the system according to stated rules), and do useful things thereby.

-- Cheers, -- Mr. d.