Re: Markov Transition Matrix

On Feb 22, 11:43 am, oswald <oswaldstu...@xxxxxxxxx> wrote:
A dynamic interurban of people shows the following Markov Transition
Matrix of residents to urban, suburban and rural areas:

__________Urban___Suburban____Rural
Urban ........... a................b...............y
suburban...... o..............q..............z
Rural ............ 1-a-o .........1-b-q ....... 1-y-z

A = 0.9
O = 0.05
B = 0.1
Q = 0.7
Y = 0.1
Z = 0.1

Solve the problem knowing that the vector answer today is
Uo ............ 10
(SUo) = (.... 40)
Ro ............ 50

What vector response to t = 2 vector and what is the answer in the
long run. Remember that
Ut
(SUt) = Aë1 ^ tX1 + Bë2 ^ tX2 + Cë3 ^ tX3

This formula is incomprehensible. First, it contains the undefined
objects e(umlaut)1^t, etc. Second, it contains a quantity 'C' that has
not been defined before, etc. So, you should avoid special characters
when posting to a newsgroup (not all newsreaders can handle them) and
you should read and edit/correct your message before posting it.

Rt

any bibliography suggestion?

What about your course textbook? If you don't have such a book, try a
Google search on 'Markov chain', to get numerous web pages that deal
with problems much like yours. Anyway, you don't need to consult a
book; you just need to know what it means to say that A = 0.9, etc. DO
YOU KNOW WHAT IT MEANS? If you do (and if you know what it means to
say that B = 0.1, etc.) then you can just apply these meanings to the
so-called "vector answer today" to get the "vector answer" at t = 1,
then re-apply to get it at t = 2, and so forth. I had to guess that by
"vector answer" you mean "population distribution".

R.G. Vickson
.

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