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From: Boris
Remote Name: 84.94.74.145
Date: 20 Aug 2005
Time: 08:10:31 -0600
Most sources define the geometric distribution as the waiting time for the occurrence of a binomial event, i.e., the number of trials up to and including the first "success". In this case the expected value is 1/p. However, Mathematica uses the definition "number of trials before the first success", and then the expected value is (1 - p)/p. Here the number of trials is one less than in the former case, and then the expected value is equal to 1/p - 1 = (1 - p)/p. A similar reasoning provides the answer for the negative binomial distribution (which is the distribution of a sum of independent and identically distributed geometric random variables).