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COS4852_2017_A3S.pdf

COS4852_2017_A3S.pdf - COS4852/A3S/0/2017 Tutorial Letter...

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BAR CODE Learn without limits. university of south africa Tutorial Letter A3S/0/2017 Machine Learning COS4852 Year module School of Computing IMPORTANT INFORMATION This document discusses the questions for Assignment 3 for COS4852 for 2017. COS4852/A3S/0/2017

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1 INTRODUCTION This document discusses the questions for Assignment 3 for COS4852 for 2017. 2 Assignment 3 2.1 Question 1 You’ve recently read a website with some interesting (but mostly useless) statistics. Among these facts are the following: • 11% of men wear glasses • 1 in every 15000 men is a librarian • 1 in every 100 men is a salesman • Every librarian wears glasses • Only 1 in every 22 salesmen wears glasses You meet Joe at a party. Joe wears glasses. You remember the data from the website and want to see if these supposedly useless facts could tell you the likelihood that Joe is a librarian. • Use Bayes’ theorem to determine the probabilities of Joe being a librarian or a salesman. • What do the results tell us? • What is interesting about the result? • Is there a better way to determine if Joe is a librarian or a salesman? 2
COS4852/A3S Discussion on Question 1 Define the following variables: L librarian G person wearing glasses S salesman Translate the five known facts to probabilities that we could use in Bayes’ theorem: P ( G ) = 0.11 P ( L ) = 0.000067 P ( S ) = 0.01 P ( G | L ) = 1 P ( G | S ) = 0.04545 From Bayes’ theorem determine the likelihood of Joe being a librarian: P ( L | G ) = P ( G | L ) × P ( L ) P ( G ) = 1 × 0.000067 0.11 = 0.00061 Similarly, determine the likelihood of Joe being a salesman: P ( S | G ) = P ( G | S ) × P ( S ) P ( G ) = 0.04545 × 0.01 0.11 = 0.0041 This means that Joe is about 15 times more likely to be a salesman than a librarian. This contrasts with our intuition about the data at hand, where the fact that all librarians wear glasses would make one think that Joe is more likely to be a librarian.

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