Transition Matrices Help

[johnsmith123]

Hello,

I've been having trouble with transition matrices problems, were the question specifies a state matrix, and im not sure wether it is the initial state matrix or for example S1, are there any specific key terms to look out for? In some questions it just seems to give no indication whatsoever if they are talking about S0, S1 etc. If so should i just assume S0? Thanks

[plato]

Hello,

I've been having trouble with transition matrices problems, were the question specifies a state matrix, and im not sure wether it is the initial state matrix or for example S1, are there any specific key terms to look out for? In some questions it just seems to give no indication whatsoever if they are talking about S0, S1 etc. If so should i just assume S0? Thanks

If a state matrix is not labelled or described as, say, the third state, then just assume it to be the initial state matrix. It doesn't matter if it actually represents the state matrix for January, the third week in December or for 2007. If you do not have to deal with any states before the one given, then you can call it the initial state matrix.

But then - is this or is it ? If you just blindly follow a rule such as   or  , and you were given a state matrix that relates to "the end of the first year", the needed state number may confuse you.

I suggest you may find it easier to think of this formula as, 
   

Thinking in this way may help show that, even if you thought that you may have been given the state matrix at the end of the 37th year, then the state matrix at the end of the 38th year =

If the question gives you an unlabelled state matrix and asks you to find , then I think you could assume you were given

[johnsmith123]

Yeah that makes sense, thanks i appreciate it