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cs-401r:axioms-of-probability-theory [2014/09/05 17:01]
cs401rpml [First Axiom]
cs-401r:axioms-of-probability-theory [2014/09/05 17:02] (current)
cs401rpml [Third Axiom]
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 == 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 == 
 If for all $0 \leq i, j$ such that $i \neq j$ the events $A_i$ and $A_j$ are disjoint (i.e., $A_i \cap A_j = \emptyset$),​ then If for all $0 \leq i, j$ such that $i \neq j$ the events $A_i$ and $A_j$ are disjoint (i.e., $A_i \cap A_j = \emptyset$),​ then
-\begin{equation} + 
-P\left(\bigcup_{j=1}^{\infty}{A_j}\right) = \sum_{j=1}^{\infty}{P\left(A_j\right)} +$P\left(\bigcup_{j=1}^{\infty}{A_j}\right) = \sum_{j=1}^{\infty}{P\left(A_j\right)}$ 
-\end{equation}+
  
 In the simple case of two variables, if $A \cap B = \emptyset$ then: In the simple case of two variables, if $A \cap B = \emptyset$ then:
-\begin{equation} + 
-P\left(A \cup B\right) = P\left(A\right) + P\left(B\right) +$P\left(A \cup B\right) = P\left(A\right) + P\left(B\right)$ 
-\end{equation}+
  
  
cs-401r/axioms-of-probability-theory.1409936515.txt.gz · Last modified: 2014/09/05 17:01 by cs401rpml
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