  There are known expressions to calculate the moments of the first passage
time in Markov chains. Nevertheless, it is commonly forgotten that in most
applications the parameters of the Markov chain are constructed using estimates
based upon empirical data and in those cases the data sample size should play
an important role in estimating the variance. Here we provide a Monte Carlo
approach to estimate the first two moments of the passage time in this
situation. We illustrate this method with an example using data from the
biological field.
