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Unformatted text preview: eneﬁts much more from learning weather forecast 47 Exact Calculaons • Require some calculus • Presented for informaon only • Such quesons 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 rao in each case? 49 Soluon • Let pR be the proporon 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 Soluon 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 rao = 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 mulple objecves • Chapters 7 and 9 • Chapter 10, natural conjugate distribuons only • Chapter 12, 14 & 15 • All addional topics covered in class, but not in the textbook, e.g. stochasc dominance 53 Next Class • Stochasc Dominance • Subjecve Probability Assessment (Chapter 8) • Pracce Exam and midterm review 54 Second half of March 12 class • There will be a demonstraon of @Risk sopware • Important new topics – Sensivity Analysis – Simulaon – Regression (review only) – Fi•ng theorecal probability distribuons 55...
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 Spring '08
 Gupta,D

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