MIT6_042JS10_lec34

MIT6_042JS10_lec34 - 1 Albert R Meyer, April 30, 2010 lec...

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Unformatted text preview: 1 Albert R Meyer, April 30, 2010 lec 12F.1 Conditional Probability & Independence Mathematics for Computer Science MIT 6.042J/18.062J lec 12F.1 Albert R Meyer, April 30, 2010 A lec 12F.2 S B 1 B 3 B 2 Law of Total Probability B 2 ! A B 3 ! A B 1 ! A lec 12F.2 Albert R Meyer, April 30, 2010 lec 12F.3 Law of Total Probability Pr{A} = Pr{B 1 ! A} + Pr{B 2 ! A} + Pr{B 3 ! A} A = (B 1 ! A) (B 2 ! A) (B 3 ! A) lec 12F.3 Albert R Meyer, April 30, 2010 lec 12F.4 Conditional Probability: A Fair Die knowledge changes probabilities: Pr{roll 1 knowing rolled odd} lec 12F.4 Albert R Meyer, April 30, 2010 lec 12F.5 Conditional Probability Pr{A|B} is the probability of event A , given that event B has occurre d: lec 12F.5 Albert R Meyer, April 30, 2010 lec 12F.8 {1,2,3,4,5,6} {1,3,5} {2,4,6} Yes No 1/2 1/2 2/3 1/3 {1} {3,5} Yes No No {2,4,6} 1 Pr{one | odd)} = Pr: 1/6 1/3 1/2 Conditional Probability: A Fair Die Pr{not one | odd} = Pr{not one | even} = Rolled 1 Rolled odd lec 12F.8 2 Albert R Meyer, April 30, 2010 lec 12F.9 Product Rule lec 12F.9 Albert R Meyer, April 30, 2010 lec 12F.10 Law of Total Probability...
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This note was uploaded on 05/27/2011 for the course CS 6.042J taught by Professor Prof.albertr.meyer during the Spring '11 term at MIT.

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MIT6_042JS10_lec34 - 1 Albert R Meyer, April 30, 2010 lec...

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