The Basic Elements of Probability

pra1 pra2 pra3 for mutually disjoint

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Unformatted text preview: A1 ∪ A2 ∪ A3 ∪ . . .) = Pr(A1 ) + Pr(A2 ) + Pr(A3 ) + . . . for mutually disjoint A1 , A2 , A3 , . . .. Math 30530 (Fall 2012) Probability basics August 28, 2013 2/2 Elements of probability 1 Experiment: involving chance, with measurable outcomes 2 Sample space Ω: exhaustive list of mutually exclusive outcomes 3 Events: subsets of outcomes representing things we’re interesting in knowing probabilities of 4 Probability law Pr: assigns to each event a number, representing how likely that event is to occur on running experiment (0 – impossible; 1 – always; 2/3 – 2 out of every 3 times). Pr satisfies three axioms of probability: 1 Pr(A) ≥ 0 for all events A 2 Pr(A ∪ B ) = Pr(A) + Pr(B ) for disjoint A, B , and more generally Pr(A1 ∪ A2 ∪ A3 ∪ . . .) = Pr(A1 ) + Pr(A2 ) + Pr(A3 ) + . . . for mutually disjoint A1 , A2 , A3 , . . .. 3 Pr(Ω) = 1 Math 30530 (Fall 2012) Probability basics August 28, 2013 2/2...
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This note was uploaded on 01/31/2014 for the course MATH 30530 taught by Professor Hind,r during the Fall '08 term at Notre Dame.

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