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Unformatted text preview: enefits much more from learning weather forecast 47 Exact Calcula-ons •  Require some calculus •  Presented for informa-on only •  Such ques-ons will not be asked in exams 48 One More Example •  A very large urn is filled with balls, 2/3rd of which are of one color and 1/3rd of another •  An individual draws 5 balls at random and finds 4 of them to be Red •  Another individual draws 20 balls at random and finds 12 of them to be Red •  Which of these two individuals should feel more confident that the urn contains 2/3rd Red balls? •  What is the odds ra-o in each case? 49 Solu-on •  Let pR be the propor-on of Red balls •  Before sampling each individual’s prior should be P(pR = 2/3) = P(pR = 1/3) = 0.5 •  Let A be the event that 4 out of 5 randomly drawn balls are Red and B be the event that 12 out of 20 randomly drawn balls are Red •  Then, we need to know P(pR=2/3 |A) and P(pR=2/3 |B) 50 Solu-on 2 2 2 P ( pR = ∩ A ) P ( A pR = ) P ( pR = ) 2 3 3 3 P ( pR = A ) = = 3 P( A) P( A) = 0.8889 •  Therefore, Odds ra-o = 0.8889/(1- 0.8889) = 8 to 1 •  Similarly, when B occurs, odds are 16 to 1 •  The second individual should be more confident even though (s)he draws a smaller percent of red balls. 51 Mid Term Exam •  In class on Wednesday, March 12 •  Closed book, closed notes •  You may bring 2 sheets of paper (8.5 by 11 inch size) with formulae that you think you will need •  If you need tables, then those will be provided 52 Syllabus •  Chapters 1- 4 excluding decisions with mul-ple objec-ves •  Chapters 7 and 9 •  Chapter 10, natural conjugate distribu-ons only •  Chapter 12, 14 & 15 •  All addi-onal topics covered in class, but not in the textbook, e.g. stochas-c dominance 53 Next Class •  Stochas-c Dominance •  Subjec-ve Probability Assessment (Chapter 8) •  Prac-ce Exam and midterm review 54 Second half of March 12 class •  There will be a demonstra-on of @Risk sopware •  Important new topics –  Sensi-vity Analysis –  Simula-on –  Regression (review only) –  Fi•ng theore-cal probability distribu-ons 55...
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