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cs-401r:axioms-of-probability-theory [2014/09/05 14:10]
ringger created
cs-401r:axioms-of-probability-theory [2014/09/05 17:02] (current)
cs401rpml [Third Axiom]
Line 1: Line 1:
 == First Axiom ==  == First Axiom == 
-The probability of any event <​math>​E</​math> ​is between 0 and 1: +The probability of any event $Eis between 0 and 1: 
-:<​math>​ + 
-0 \leq P\left(E\right) \leq 1 +$0 \leq P\left(E\right) \leq 1$
 == Second Axiom ==  == Second Axiom == 
-The probability of the entire sample space <​math>​\Omega</​math> ​(equivalently,​ the "​certain event"​) is 1. +The probability of the entire sample space $\Omega(equivalently,​ the "​certain event"​) is 1. 
-:<​math>​ + 
-P\left(\Omega\right) = 1 +$P\left(\Omega\right) = 1$ 
 == Third Axiom ==  == 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 +If for all $0 \leq i, jsuch that $i \neq jthe events ​$A_iand $A_jare disjoint (i.e., ​$A_i \cap A_j = \emptyset$), then 
-:<​math>​ + 
-P\left(\bigcup_{j=1}^{\infty}{A_j}\right) = \sum_{j=1}^{\infty}{P\left(A_j\right)} +$P\left(\bigcup_{j=1}^{\infty}{A_j}\right) = \sum_{j=1}^{\infty}{P\left(A_j\right)}
 +In the simple case of two variables, if $A \cap B = \emptyset$ then: 
 +$P\left(A \cup B\right) = P\left(A\right) + P\left(B\right)$ 
-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.1409926221.txt.gz · Last modified: 2014/09/05 14:10 by ringger
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