  This paper calculates probability distributions modeling the Luria-Delbr\"uck
experiment. We show that by thinking purely in terms of generating functions,
and using a 'backwards in time' paradigm, that formulas describing various
situations can be easily obtained. This includes a generating function for
Haldane's probability distribution due to Ycart. We apply our formulas to both
simulated and real data created by looking at yeast cells acquiring an
immunization to the antibiotic canavanine.
  This paper is somewhat incomplete, having been last significantly modified in
March 29, 2014. However the first author feels that this paper has some
worthwhile ideas, and so is going to make this paper publicly available.
