Class Meeting 05

Class Meeting 05 - CHEN 3010 Applied Data Analysis Class...

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CHEN 3010 Applied Data Analysis Class Meeting #5 September 7, 2004 Topics Basic concepts of probability Ways of counting Permutations Combinations Reading for Thursday: pages 61-73 Homework #2 due Thursday Distribution functions Discrete random variables Continuous random variables
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Axioms S: set of all possible events [] 0 PA A: any event in S [ ] 1 PS = If 123 ,,, AA A are mutually exclusive (independent) then [ ] [ ] [ ] [ ] 1 2 3 PA A A PA PA ∪∪∪ = + + +  Theorems [ ] 0 P φ= where φ is null event [ ] [ ] 1 = where A is complement of A S A A union -- or Venn diagrams help understanding
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Addition Rule [ ] [ ] [ ] [ ] 12 1 2 PA A A ∪= + 1 A 2 A AA Conditional Probability [ ] [ ] 21 1 A PAA =  Independence [ ] [ ] [ ] 1 2 A ∩= Multiplication Rule [ ] [ ] 1 2 1 A P A A intersection -- and probability that A2 will occur, given that A1 does occur
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Example: 10-coin toss [ ] [ ] [ ] [ ] P 10 heads P 1 head P 1 head P 1 head 10 times = ⋅→ [ ] [ ] 10 10 1 P 10 heads P 1 head 0.5 1024 = = = Example: blood donations [ ] P blood from paid donor 0.67
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Class Meeting 05 - CHEN 3010 Applied Data Analysis Class...

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