7406_Solution1 - ISyE 7406, Spring-2007 Instructor:...

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ISyE 7406, Spring-2007 Instructor: Kwok-Leung Tsui Assignment # 1 (Solution) Question 1: If you use this command ’home < - read.csv(”hmeq.csv”, na.strings=” ”)’, you may not be able to get the correct number of rows after removing ”NA” cells by ’complete.cases’. Use ’home < - read.csv(”hmeq.csv”, na.strings=”” )’ (no space) instead. Question 2: We have X 0 = ± x 01 x 02 G ( μ 0 , Σ 0 ) , X 1 = ± x 11 x 12 G ( μ 1 , Σ 1 ) where X 0 is for y = 0 and X 1 is for y = 1. Suppose the new data is X = x = ± x 1 x 2 . Recall that the Bayes classifier is ˆ G ( X ) = max g G Pr ( g | X = x ). In this ques- tion, G = { 0 , 1 } . Therefore, the Bayes decision boundary will be Pr ( g = 0 | X = x ) = Pr ( g = 1 | X = x ) = 1 / 2. Using Bayes rule and Pr ( g = 0) = Pr ( g = 1) = 1 / 2, Pr ( g = 0 | X = x ) = Pr ( X = x | g = 0) Pr ( g = 0) Pr ( X = x | g = 0) Pr ( g = 0) + Pr ( X = x | g = 1) Pr ( g = 1) = 1 2 π k Σ 0 k 1 / 2 e - 1 2 ( x - μ 0 ) T Σ - 1 0 ( x - μ 0 ) 1 2
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This note was uploaded on 11/13/2010 for the course ISE 680 taught by Professor Santanu during the Spring '10 term at Purdue University Calumet.

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7406_Solution1 - ISyE 7406, Spring-2007 Instructor:...

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