Markov model on a sequence of numbers

[iheadset]

Dear Sir,
Assuming that my lottery machine can generate 10 numbers (0..9), in which 0 and 9 are supposed to be starting and ending states of my Markov chain. I apply Markov chain to model each number appearance because I would want to modify the random generation process into, say, my own process, such that each currently output number will show up in dependence of the previously generated number.
Now I would like to run my generator 1000 times and given the probability for any number to reach the end state is x, how can I calculate the sum of probabilities of all integral sequences then ?
Thank you Sir.

 

[chiro]

Hey iheadset.

When you say sum of probabilities do you mean the sum of them at each transition point or the sum of events at the final transition?

 

[iheadset]

Hey iheadset.

When you say sum of probabilities do you mean the sum of them at each transition point or the sum of events at the final transition?

Yes, that is right Sir. I would like to find that sum.

 

[chiro]

That means you are looking at a T + T^2 + T^3 + ... + T^n matrix to find the sum of these transition matrices.

If you supply an initial probability as your vector and apply it to the above sum there is only one more thing to do - which is to find intersections in events and remove them as they will be "double counted".

You will probably have to resort to the Markov property to do this and generate identities which you can use to find them.

 

[mack jackson]

'You can try permutation and combinations'. I think it is the easiest method to solve the problem and also you get approximate method. You can try this.