math319_S10_WS2

# math319_S10_WS2 - P F-P E ∩ F Proof C6 For any ﬁnite...

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Probability and Statistics – Math319, Spring 2010 Consequences of the Axioms Jan 28, 2010 ( C1 ) P ( ) = 0 . Proof. ( C2 ) For any ﬁnite sequence of mutually exclusive events E 1 ,E 2 ,...,E n , P n [ i =1 E i ! = n X i =1 P ( E i ) . Proof.

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( C3 ) For every event E , P ( E c ) = 1 - P ( E ) . Proof. ( C4 ) ( Monotonicity ) If E F , then P ( E ) P ( F ) . Proof. ( C5 ) For any events E,F , P ( E F ) = P ( E ) +

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Unformatted text preview: P ( F )-P ( E ∩ F ) . Proof. ( C6 ) For any ﬁnite sequence of events E 1 ,E 2 ,...,E n , P n [ i =1 E i ! ≤ n X i =1 P ( E i ) . Proof. ( C7 ) ( Monotone limits ) If E n ↑ E or E n ↓ E , then lim n →∞ P ( E n ) = P ( E ) . Proof....
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## This note was uploaded on 10/14/2010 for the course MATH 319 taught by Professor Clionagolden during the Spring '10 term at Bard College.

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math319_S10_WS2 - P F-P E ∩ F Proof C6 For any ﬁnite...

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