week2_F10 - Online EE131A TA session : Week 2 TA: Ni-Chun...

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nline EE131A Online EE131A TA session : Week 2 TA: Ni-Chun Wang nichun@ucla.edu
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Review : Axioms of Probability (1) Sample space S . Events A, B S . • I. 0 P( A ) • II. P( S ) = 1 • III. If A B = , then P( A B ) = P( A ) + P( B ). I’ If are mutually disjoint (i e III . If A 1 , A 2 , …, are mutually disjoint (i.e., A i A j = , for all i and j , i j), then () i=1 i i=1 i . P P ⎛⎞ = ⎜⎟ ⎝⎠ A A 2
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Review : Axioms of Probability (2) Corollaries: • 1. P( A C ) = 1 – P( A ). (since A A C = S ) • 2. P( A ) 1. • 3. P( ) = 0. (since S C = ) ( = P( +P( ( 4. P( A B ) P( A ) + P( B ) P( A B ) . P( A B C ) = P( A ) + P( B ) + P( C ) – P( A B ) – P( B C ) – P( A C ) + P( A B C ). • 5. If A B , then P( A ) P( B ). 3
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• 1. Let the events A and B have P(A) = x, P(B) = y and P(A B) = z. Find P(A B), P(A c B c ), P(A c B c ), P(A B c ), P(A c B). – P(A B) = P(A) + P(B) – P(A B) => z = x + y – P(A B) => P(A B) = x + y – z. –P (A c B c ) = P((A B) c ) = 1 - P(A B) = 1 – z c B c ) = P((A B) c ) = 1 - P(A B) = 1 – (x + y – z) DeMorgan’s Rules ( A B c ) = P(A) – P(A B) = x – (x + y – z) = z – y P(A c B) = P(A c ) +P(B) – P(A c B) = P(A c ) +P(B) –(P(B) – P(A B)) = 1 – z + y ( A c B) = P((A B c ) c ) = 1 – P(A B c ) = 1 – z + y 4
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• 2. A box contains 10 white balls, 20 reds and 30
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This note was uploaded on 11/05/2010 for the course ELECTRICAL EE131A taught by Professor Kungyao during the Spring '10 term at UCLA.

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week2_F10 - Online EE131A TA session : Week 2 TA: Ni-Chun...

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