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First Axiom

The probability of any event $E$ is between 0 and 1: \begin{equation} 0 \leq P\left(E\right) \leq 1 \end{equation}

Second Axiom

The probability of the entire sample space $\Omega$ (equivalently, the “certain event”) is 1. \begin{equation} P\left(\Omega\right) = 1 \end{equation}

Third Axiom

If for all <math>0 \leq i, j</math> such that <math>i \neq j</math> the events <math>A_i</math> and <math>A_j</math> are disjoint (i.e., <math>A_i \cap A_j = \emptyset</math>), then :<math> P\left(\bigcup_{j=1}^{\infty}{A_j}\right) = \sum_{j=1}^{\infty}{P\left(A_j\right)} </math>

In the simple case of two variables, if <math>A \cap B = \emptyset</math> then: :<math>P\left(A \cup B\right) = P\left(A\right) + P\left(B\right)</math>

cs-401r/axioms-of-probability-theory.1409936091.txt.gz · Last modified: 2014/09/05 16:54 by cs401rpml
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