probability in Markov chain

Given, a state sequence (100 elements) of two different states '1' or '2'. find the probability of occurance of '1' and '2'(P1 and P2).

Also find the probability of occurance of P11,P12,P21,P22 where P11(probability of the state remaining in the state 1 during a transition and similarly others) represents the elements of state transition probability matrix.

Any sort of help would be appreciated.

Thanks & Regards

[SATYANARAYANA R]

please provide

step- by -step solution

Answer 1

[Fangjun Jiang]

I can write the code in a couple of minutes. But let's see if you can help me to help you.

1. Generate a vector of 100x1 or 1x100. The data is a random distribution of '1' and '2'. You can use rand(). Or randint() is even better.

2. set your P=zeros(2,2)

3. Go through a for-loop. If the vector value goes from 1 to 1, P(1,1) is increased by 1. If the values goes from 1 to 2, P(1,2) is increased by 1. And so on.

4. At the end, divide P by 100 (your data length), you get your probability matrix.

EDIT This is incorrect. Should divide the first row by the total number of 1s and divide the second row by the total number of 2s.

Start writing your MATLAB code, if you have particular questions regarding using MATLAB functions, or M-script syntax. People here would love to help you.

[SATYANARAYANA R]

please provide MATLAB CODES

[Walter Roberson]

SATYANARAYANA R: it is a homework question, and we avoid giving complete solutions to homework questions. Fangjun has given an outline of what you need to do. You should make a start at the code, and you can come back and ask specific questions if you have trouble getting your code to work.