user366312
Gold Member
 66
 2
 Summary

I know how to mathematically calculate the probability of various Markov Properties.
But, how can I calculate Markov probability from data?
Suppose, I have a Markov Chain as follows:
##S=\{1, 2\}##
##
\alpha = \begin{bmatrix}
0.5&0.5\end{bmatrix}
##
##
P =
\begin{bmatrix}
0.5&0.5\\
0&1
\end{bmatrix}
##
And, the following data regarding 5 steps of Markov Chain taken 12 times:
How can I calculate,say, ##P(X_1 = 1X_0 = 1)## and ##P(X_5 = 2X_2 = 1)## from this table?
Kindly, explain your answer.
##S=\{1, 2\}##
##
\alpha = \begin{bmatrix}
0.5&0.5\end{bmatrix}
##
##
P =
\begin{bmatrix}
0.5&0.5\\
0&1
\end{bmatrix}
##
And, the following data regarding 5 steps of Markov Chain taken 12 times:
Markov Chain:
Steps 1 2 3 4 5

1 2 2 1 1 1
2 1 1 1 1 1
3 1 1 1 1 1
4 1 1 1 1 1
5 2 2 2 1 1
6 2 2 2 1 1
7 1 1 1 1 1
8 1 1 1 1 1
9 1 1 1 1 1
10 2 2 2 2 2
11 1 1 1 1 1
12 1 1 1 1 1
Kindly, explain your answer.