  Many random transport phenomena, such as radiation propagation,
chemical/biological species migration, or electron motion, can be described in
terms of particles performing {\em exponential flights}. For such processes, we
sketch a general approach (based on the Feynman-Kac formalism) that is amenable
to explicit expressions for the moments of the number of collisions and the
residence time that the walker spends in a given volume as a function of the
particle equilibrium distribution. We then illustrate the proposed method in
the case of the so-called {\em rod problem} (a 1d system), and discuss the
relevance of the obtained results in the context of Monte Carlo estimators.
