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This paper calculates probability distributions modeling the Luria-Delbr\"uckexperiment. We show that by thinking purely in terms of generating functions,and using a 'backwards in time' paradigm, that formulas describing varioussituations can be easily obtained. This includes a generating function forHaldane's probability distribution due to Ycart. We apply our formulas to bothsimulated and real data created by looking at yeast cells acquiring animmunization to the antibiotic canavanine.  This paper is somewhat incomplete, having been last significantly modified inMarch 29, 2014. However the first author feels that this paper has someworthwhile ideas, and so is going to make this paper publicly available.

Estimation of Mutation Rates from Fluctuation Experiments via Probability Generating Functions