Lecture6__8211_Chapter2

# Lecture6__8211_Chapter2 - Lecture 6 Chapter 2 Wednesday,...

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Lecture 6 – Chapter 2 Wednesday, September 10 th

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Probability ± The objective of probability is to assign to each event A, a number P(A), which is called probability of the event A and will give a precise measure of the chance that A will occur.
Axiom of Probability ± Axiom 1: For any event A, ± Axiom 2: ± Axiom 3: If is an infinite collection of disjoint events then ( ) 0 PA ( ) 1 P = S 12 , ,... AA () ( ) 1 ... i i P P A = ∪∪ =

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Proposition ± From the Axioms of Probability we can prove that . This also implies that Axiom 3 is valid for a finite collection of events. ± Proof? ( ) 0 P ∅ =
Probability Properties ± For any event A, ± Proof? ( ) ( ) 1 c P AP A =−

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Probability Properties ± For any events A and B, ± Proof? ( ) ( ) ( ) ( ) PA B PB B ∪= +
Equally possible outcomes ± In many experiments, like tossing a coin or

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## This note was uploaded on 09/23/2009 for the course STAT 318 taught by Professor Staff during the Fall '08 term at Penn State.

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Lecture6__8211_Chapter2 - Lecture 6 Chapter 2 Wednesday,...

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