3.3.5 How to find number of visits to a transient state?

Number of visits to transient state is a geometric distribution.

\[ \Pr \left ( n\right ) =f_{ii}^{n-1}\left ( 1-f_{ii}\right ) \]

The expected number of visits to transient state \(i\) is

\[ E\left ( X\right ) =\frac {1}{1-f_{ii}}\]

where \(f_{ii}\) is the probability of visiting state \(i\) if chain starts in state \(i\)