#ECE313

Axioms of Probability(概率公理)

Terms

  • $\Omega$ : Denote the sample space(样本空间)，表明所有可能结果的集合
  • Event(事件): An event is a subset of the sample space $\Omega$
  • Outcome: denote as $\omega$ is an element of sample space
  • Complement of an event(事件的补集): denote as $E^{c}$
  • Exclusive(互斥事件) & Partition of a sample space

  • The number of elements of in a set is called the cardinality of the set
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  • Experiment modelled by triplet
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Axioms

Event Axioms

The set of events, $F$ is required to satisfy the following axioms
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  • 利用公理三基于已定义的事件推出新的事件（将新定义的命题进行拆解）
    Property:
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Probability Axioms

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注意：将互斥事件加和得到总概率只适用于有限集或者可数无限集，不适用于不可数无限集