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Unformatted text preview: Study Sheet for Math 3225, Exam 1, Fall 2010 October 8, 2010 1. Know basic definitions and results from set theory; for example, know the two forms of de Morgans law, know distributive rule of intersection and union (whichs says A ( B C ) = ( A B ) ( A C ) and A ( B C ) = ( A B ) ( A C )). Also know injective, surjective, bijective maps, and how to prove that various maps have these properties. 2. Know the definition of a sigma algebra: S is a sigma-algebra means that i) S contains the empty set. ii) If A S , then A S iii) If A 1 ,A 2 ,... is a countable collection of sets in S , then their union blongs to S . 3. Know the Kolmogorov axioms of probability: P : [0 , 1] is a probability measure from the sigma-algebra consisting of certain subsets of S (the sample space) if i) P ( S ) = 1 ii) If A 1 ,A 2 ,... is a disjoint collection of sets in , then P ( A 1 A 2 ) = P ( A 1 ) + P ( A 2 ) + ....
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