H3 - Statistical Pattern Recognition University of...

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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 one-dimensional two-category classification problem with equal priors, P ( 1 ) = P ( 2 ) = 1 / 2, where the densities have the form p ( x | i ) = braceleftbigg x < i e- i x x where the 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 1 and 2 respectively. Find the maximum-likelihood values 1 and 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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H3 - Statistical Pattern Recognition University of...

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