# STATSLIDE2 - AXIOMATIC PROBABILITY AND POINT SETS The...

This preview shows pages 1–3. Sign up to view the full content.

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: AXIOMATIC PROBABILITY AND POINT SETS The axioms of Kolmogorov. Let S denote an event set with a probability measure P defined over it, such that probability of any event A ⊂ S is given by P ( A ). Then, the probability measure obeys the following axioms: (1) P ( A ) ≥ , (2) P ( S ) = 1 , (3) If { A 1 ,A 2 ,...A j ,... } is a sequence of mutually exclusive events such that A i ∩ A j = ∅ for all i,j , then P ( A 1 ∪ A 2 ∪···∪ A j ∪··· ) = P ( A 1 ) + P ( A 2 ) + · · · + P ( A j ) + · · · . The axioms are supplemented by two definitions: (4) The conditional probability of A given B is defined by P ( A | B ) = P ( A ∩ B ) P ( B ) , (5) The events A,B are said to be statistically independent if P ( A ∩ B ) = P ( A ) P ( B ) . This set of axioms was provided by Kolmogorov in 1936. 1 The rules of Boolean Algebra. The binary operations of union ∪ and intersection ∩ are roughly analogous, respectively, to the arithmetic operations of addition + and multiplication × , and they obey a similar set of laws which have the status of axioms: Commutative law: A ∪ B = B ∪ A , A ∩ B = B ∩ A , Associative law: ( A ∪ B ) ∪ C = A ∪ ( B ∪ C ), ( A ∩ B ) ∩ C = A ∩ ( B ∩ C ), Distributive law: A ∩ ( B ∪ C ) = ( A ∩ B ) ∪ ( A ∩ C ),...
View Full Document

## This note was uploaded on 03/02/2012 for the course EC 2019 taught by Professor D.s.g.pollock during the Spring '12 term at Queen Mary, University of London.

### Page1 / 7

STATSLIDE2 - AXIOMATIC PROBABILITY AND POINT SETS The...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online