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The chapter, after recalling the axiomatic definition of probability as opposed to that of frequency of events, illustrates their conceptual differences with a number of elementary examples. Subsequently, showing that probabilities and frequencies share some mathematical properties, it is clarified too that zero-frequency and zero-probability cases have a substantially different meaning; this invalidates the von Mises attempt to define probability as limit of frequencies.

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Probability and Frequency

  • 章节

  • 发表日期：

    2025年

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  • Fernando Sansò,
  • Alberta Albertella

摘要

The chapter, after recalling the axiomatic definition of probability as opposed to that of frequency of events, illustrates their conceptual differences with a number of elementary examples. Subsequently, showing that probabilities and frequencies share some mathematical properties, it is clarified too that zero-frequency and zero-probability cases have a substantially different meaning; this invalidates the von Mises attempt to define probability as limit of frequencies.