# 05 x5 x95 y05 y5 y95 assign probabili es 0185 to

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## This document was uploaded on 03/12/2014 for the course IE 5545 at Minnesota.

Ask a homework question - tutors are online