A probabilistic derivation of Stirling's formula
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Stirling's formula is one of the most frequently used results from asymptotics. It is used in probability and statistics, algorithm analysis and physics. In this thesis we shall give a new probabilistic derivation of Stirling's formula. Our motivation comes from sampling randomly with replacement from a group of n distinct alternatives. Usually a repetition will occur before we obtain all n distinct alternatives consecutively. We shall show that Stirling's formula can be derived and interpreted as follows: as n (to infinity) the expected total number of distinct alternatives we must sample before all n are obtained consecutively is asymptotically equal to the expected number of attempts we make to obtain all n distinct alternatives consecutively times the expected number of distinct alternatives obtained per attempt.
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