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cs-401r:axioms-of-probability-theory [2014/09/05 16:55] cs401rpml [Third Axiom] |
cs-401r:axioms-of-probability-theory [2014/09/05 17:02] cs401rpml [Second Axiom] |
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== First Axiom == | == First Axiom == | ||

The probability of any event $E$ is between 0 and 1: | The probability of any event $E$ is between 0 and 1: | ||

- | \begin{equation} | + | |

- | 0 \leq P\left(E\right) \leq 1 | + | $0 \leq P\left(E\right) \leq 1$ |

- | \end{equation} | + | |

== Second Axiom == | == Second Axiom == | ||

The probability of the entire sample space $\Omega$ (equivalently, the "certain event") is 1. | The probability of the entire sample space $\Omega$ (equivalently, the "certain event") is 1. | ||

- | \begin{equation} | + | |

- | P\left(\Omega\right) = 1 | + | $P\left(\Omega\right) = 1$ |

- | \end{equation} | + | |

== Third Axiom == | == Third Axiom == |