{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

352InclExclHandout

# 352InclExclHandout - event decompositions Therefore Hence...

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

Inclusion - Exclusion Theorem: For let denote the event that exactly m among the events occur simultaneously. Then , where . (Note that the formula for contains summands.) Proof: Let be the partition of the sample space determined by the possible events of the form where each is either . For let and let such that . Then . Now consider E -event probabilities. Since the right hand side sum includes if and only if exactly of the summands in the expression for include in their

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.

Unformatted text preview: event decompositions. Therefore, Hence Observe that then Therefore, Q.E.D. Theorem: For let denote the event that at least m among the events occur simultaneously. Then Proof: Define the B-events as in the previous theorem. so the formula is valid when . Now assume the formula is valid for fixed and consider Therefore, the validity of the formula for fixed implies the validity of the formula for . Hence, the theorem is proved by induction. Q.E.D....
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

352InclExclHandout - event decompositions Therefore Hence...

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

View Full Document
Ask a homework question - tutors are online