L05_S10 - AMS 311, Lecture 5, Spring Semester, 2010 2.4...

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AMS 311, Lecture 5, Spring Semester, 2010 2.4 Some Simple Propositions Proposition 4.1. For any event E , ) ( 1 ) ( E P E P C - = . Proposition 4.2. If F E , then ) ( ) ( F P E P . Also, if F E , then ) ( ) ( ) ( ) ( E P F P FE P E F P C - = = - . Proposition 4.3. If E and F are any two events , ) ( ) ( ) ( ) ( EF P F P E P F E P - + = . Boole’s (Bonferroni’s) Inequality If E and F are any two events , ) ( ) ( ) ( F P E P F E P + . This is a crucial fact to have handy in applied statistical work. If E and F are any two events , ) ( ) ( ) ( C EF P EF P E P + = . Odds in favor of an event A are r to s if s r r A P + = ) ( . Odds against an event A are r to s , if s r s A P + = ) ( . If p A P = ) ( , then the odds in favor of A are p to p - 1 . Generalizations of probability of union of two events: If 3 2 1 , , E E E are any three events, then ). ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( 3 2 1 3 2 3 1 2 1 3 2 1 3 2 1 E E E P E E P E E P E E P E P E P E P E E E P + - - - + + = Example. A doctor has 520 patients, of which
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This note was uploaded on 03/22/2010 for the course AMS 311 taught by Professor Tucker,a during the Spring '08 term at SUNY Stony Brook.

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L05_S10 - AMS 311, Lecture 5, Spring Semester, 2010 2.4...

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