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# lecture2 - Stat 302 Introduction to Probability Jiahua Chen...

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Stat 302, Introduction to Probability Jiahua Chen January 2011 Jiahua Chen () Lecture 2 January 2011 1 / 1

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Axioms of Probability We often have good ideas on assigning a probability to a possible outcome of a random outcome. For example It will snow tomorrow with probability 80%. When you toss a coin, the chance of the outcome being head is 50% We have problems in other occasions: Canucks will win the next game with probability 99%. Some may not agree with me, and there is hardly a truth on the size of this probability. We could have a verbal war. Or let us only work on rules how to assign probabilities, not on how large the probability of each event has. Jiahua Chen () Lecture 2 January 2011 2 / 1
Axioms of Probability Consider a random experiment with sample space S . We assign a number P ( E ) to each event E such that P ( E ) satisfies the following 3 axioms: Axiom 1 For any event E , 0 P ( E ) 1 Axiom 2 The sample space has probability 1: P ( S ) = 1 Axiom 3 . For any sequence of events { E i } i = 1 , such that E i E j = whenever i 6 = j , P ( i = 1 E i ) = i = 1 P ( E i ) Jiahua Chen () Lecture 2 January 2011 3 / 1

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Direct Consequences P ( ) = 0.
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lecture2 - Stat 302 Introduction to Probability Jiahua Chen...

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