The search for extraterrestrial intelligence (SETI) has been heavily influenced by solutions to the Drake Equation, which returns an integer value for the number of communicating civilizations resident in the Milky Way, and by the Fermi Paradox, glibly stated as: ‘If they are there, where are they?’. Both rely on using average values of key parameters, such as the mean signal lifetime of a communicating civilization. A more accurate answer must take into account the distribution of stellar, planetary and biological attributes in the galaxy, as well as the stochastic nature of evolution itself. This paper outlines a method of Monte Carlo realization that does this, and hence allows an estimation of the distribution of key parameters in SETI, as well as allowing a quantification of their errors (and the level of ignorance therein). Furthermore, it provides a means for competing theories of life and intelligence to be compared quantitatively.