{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# lect7 - INDEPENDENCE OF TWO EVENTS MULTIPLICATION RULE FOR...

This preview shows pages 1–4. Sign up to view the full content.

INDEPENDENCE OF TWO EVENTS MULTIPLICATION RULE FOR INDEPENDENT EVENTS INDEPENDENCE FOR THREE EVE Outline INDEPENDENCE OF TWO EVENTS MULTIPLICATION RULE FOR INDEPENDENT EVENTS INDEPENDENCE FOR THREE EVENTS INDEPENDENCE OF SEVERAL EVENTS 1 / 11 Xinghua Zheng Lect 7: Independence of Events

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

View Full Document
INDEPENDENCE OF TWO EVENTS MULTIPLICATION RULE FOR INDEPENDENT EVENTS INDEPENDENCE FOR THREE EVE INDEPENDENCE OF TWO EVENTS An event B is said to be independent of an event A (with P [ A ] > 0 and P [ A c ] > 0) if the occurrence or nonoccurence of A has no bearing on the chance for B to occur. Otherwise B is said to depend on A. More precisely, B is independent of A if P [ B | A ] = P [ B | A c ] . In general, what is the relation between P [ B ] , P [ B | A ] , and P [ B | A c ] ? P [ B ] = . If B is independent of A, then P [ B ] = = . 2 / 11 Xinghua Zheng Lect 7: Independence of Events
INDEPENDENCE OF TWO EVENTS MULTIPLICATION RULE FOR INDEPENDENT EVENTS INDEPENDENCE FOR THREE EVE EXAMPLE: TOSS TWO DICE B is independent of A P [ B | A ] = P [ B | A c ] P [ B ] = P [ B | A ] . Two fair dice are to be rolled. Let A be the event that their sum is 6: A = { ( 1 , 5 ) , ( 2 , 4 ) , ( 3 , 3 ) , ( 4 , 2 ) , ( 5 , 1 ) } B be the event that the first die is a 4. Is B independent of A? P [ B | A ] = ; P [ B ] = . As above, but change A to the event that the sum is 7. A = { ( 1 , 6 ) , ( 2 , 5 ) , ( 3 , 4 ) , ( 4 , 3 ) , ( 5 , 2 ) , ( 6 , 1 ) } Is B independent of A ?

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern