I have the following probability matrix:
\begin{pmatrix} 0 & 0.75 & 0.25\\ 0.75 & 0.25 & 0\\ 1 & 0 &0 \end{pmatrix}
I want to calculate the expected number of times we visit state 3 before hitting state 2.
Now, I know that if I were looking at the probabilities I would use the following system:
\begin{cases} h_1= 0.75h_2 + 0.25h_3 \\ h_2=0 \\ h_3=1 \end{cases}
but I do not know how to translate this into the expected number of visits.