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Unformatted text preview: Statistical Pattern Recognition University of Maryland, College Park September 24, 2009 Professor Rama Chellappa Handout 3 Homework 3 This problem set is due Thursday October 1 at 11:00AM . 1. Consider a onedimensional twocategory classification problem with equal priors, P ( ω 1 ) = P ( ω 2 ) = 1 / 2, where the densities have the form p ( x  ω i ) = braceleftbigg x < θ i e θ i x x ≥ where the θ i for i = 1 , 2, are positive but unknown parameters. (a) Confirm that the distributions are normalized. (b) The following data were collected: D 1 = { 1 , 5 } and D 2 = { 3 , 9 } for ω 1 and ω 2 respectively. Find the maximumlikelihood values ˆ θ 1 and ˆ θ 2 . (c) Given your answer to part (b), determine the decision boundary x * for minimum classification error. Be sure to state which category has higher values than x * , and which category lower values than x * . (d) What is the expected error of your classifier in part (c)?...
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This note was uploaded on 10/26/2009 for the course CMSC 828 taught by Professor Staff during the Fall '05 term at Maryland.
 Fall '05
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