Lecture4

Lecture4 - ECE 340 Probabilistic methods in engineering...

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ECE 340 Probabilistic methods in engineering Lecture 4 Jean Liu Email: [email protected]
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Reading • This class: Section 2.5 • Next class: Section 2.6
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outline • Independence – Definition derived from conditional probability – General definition for two events – General definition for three events – General definition for N events • Examples
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Independence of events • If the occurrence of an event A doesn’t alter the probability of the occurrence of other event B, then, event A is independent of event B. [] [ | ] [ ] [ ] P AB PB PB A PA B PB == ∩=
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• P[A|B] = ? [] [ ] [ ] [|] [ ] PA B PAPB P AB P A PB == = Note: P[A] 0 P[B] 0
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Example1 • A ball is selected from an urn including 1 2 3 4 A: Black balls { (1,b), ( 2,b) } B: Even-numbered balls {(2,b), (4,w) } C: Greater than 2 balls { {3,w,), (4,w)} ½ ½ ½ Are events A and B independent? Are events A and C independent?
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[] ? PA B ∩= 1 { ( 2 , ) } 4 11 1 [ ] 22 4 B b P b == =⋅ = [|] ? B = {(2, )} 1/4 1 {(2, ),(4, )} 1/2 2 1 [ ] {(1, )(2, )} 2 PA B P b PAB PB P b w PA P b b = = Events A and B are independent
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Events A and C ?
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This note was uploaded on 02/10/2010 for the course TBE 2300 taught by Professor Cudeback during the Spring '10 term at Webber.

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Lecture4 - ECE 340 Probabilistic methods in engineering...

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