help with a probability matrix/markov process

[rocadelpunk]

Note: This is an extra credit problem if this influences your decision to post
I'm not asking for the answer, just a step in right direction.
Not supposed to use eigenvalues and eigenvectors

Picture

above is the picture of the problem. you assume the person starts at first intersection and can only move to adjacent intersections...there are two parts when 1 and 3 are/aren't adjacent. Assume you don't stay at same spot.

Anyway, how I understood to get my probability matrix... So I have an 8x8 matrix where row's are "from" and columns are "to"

so from 1 to 1 would be 0 since you start at one. In the picture the only adjacent intersections are 2 and 4...so in columun 2 and 4 of row 1 I put a 1/2 and everything else in row 1 has a 0

same thing with "from" 2 to something else...when at intersection 2 ...only 1 and 5 are adjacent so columns 1 and 5 of row 2 would have a 1/2 rest of row 2 would be 0...

this carries on where if there are three possibilities it'd be 1/3 and if 4...1/4th

is this correct?

The reason I ask is b/c the professor asked if it stabilizes to find what vector...

Well I assume to find if it stabilizes...that's the whole if a= my matrix

then i'd go till A^i+1 - A^i = 0

when I put the thing in matlab it stabilizes...but not to 0...is it wrong to say it stabilizes if it doesn't go to 0? After a^26-a^25 ...the values are the same.

If someone could shed a little light on situation : P

Thanks!

 

[cchen]

i hate stochastic models... but maybe when i get home i can look at some of my notes to jog my memory. seems like a basic markov chain problem

 

[rocadelpunk]

thanks...the professor didn't really cover this, just gave us basic overview one day...never assigned any problems just moved onto something else.

 

[rocadelpunk]

hmm so I did the part where 1 and 3 are considered adjacent and I think that may be where the thing kinda heads toward 0...

: (

 

[rocadelpunk]

bump :0