Lecture4

# Lecture4 - ECE 340 Probabilistic methods in engineering...

This preview shows pages 1–9. Sign up to view the full content.

ECE 340 Probabilistic methods in engineering Lecture 4 Jean Liu Email: [email protected]

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Reading • This class: Section 2.5 • Next class: Section 2.6
outline • Independence – Definition derived from conditional probability – General definition for two events – General definition for three events – General definition for N events • Examples

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 == ∩=
• P[A|B] = ? [] [ ] [ ] [|] [ ] PA B PAPB P AB P A PB == = Note: P[A] 0 P[B] 0

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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?
[] ? 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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Events A and C ?
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 02/10/2010 for the course TBE 2300 taught by Professor Cudeback during the Spring '10 term at Webber.

### Page1 / 23

Lecture4 - ECE 340 Probabilistic methods in engineering...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online