18_05_lec5

18_05_lec5 - 18.05 Lecture 5 February 14, 2005 2.2...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 18.05 Lecture 5 February 14, 2005 2.2 Independence of events. P ( A B ) = P ( AB ) P ( B ) ; | Definition- A and B are independent if P ( A B ) = P ( A ) | P ( AB ) P ( A B ) = = P ( A ) P ( AB ) = P ( A ) P ( B ) | P ( B ) Experiments can be physically independent (roll 1 die, then roll another die), or seem physically related and still be independent. Example: A P ( A 1 ) = { } . P ( B 2 { 1 , 3 } = P ( AB 1 3 odd , B ) = ) = , therefore independent. = = { 1, 2, 3, 4 } . Related events, but independent. .AB = 2 3 2 P ( AB ) = 1 3 2 Independence does not imply that the sets do not intersect. Disjoint = Independent. If A, B are independent, find P ( AB c ) P ( AB ) = P ( A ) P ( B ) AB c = A \ AB , as shown: so, P ( AB c ) = P ( A ) P ( AB ) = P ( A ) P ( A ) P ( B ) = P ( A )(1 P ( B )) = P ( A ) P ( B c ) therefore, A and B c are independent as well. similarly, A c and B c are independent. See Pset 3 for proof....
View Full Document

Page1 / 3

18_05_lec5 - 18.05 Lecture 5 February 14, 2005 2.2...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online