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The Вayes decision functions d;(x) = p(x|w;) p(w;), j = 1, 2, ... w; were derived using a 0 - 1 loss function. Prove %3D that these decision functions minimize the probability of error. Find p(c) and show that p(c) is maximum, when p(x|w;) p(w;) is maximum. Assume that the probability of error p(e) is 1 - p(c) where p(c) is probability of being correct and for a pattern vector x belonging to class W¡, p(c|x) = p(w;|x).

The Вayes decision functions d;(x) = p(x|w;) p(w;), j = 1, 2, ... w; were derived using a 0 - 1 loss function. Prove %3D that these decision functions minimize the probability of error. Find p(c) and show that p(c) is maximum, when p(x|w;) p(w;) is maximum. Assume that the probability of error p(e) is 1 - p(c) where p(c) is probability of being correct and for a pattern vector x belonging to class W¡, p(c|x) = p(w;|x).

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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The Ваyes decision functions d;(x) = p(x|w;) p(w;), j = 1, 2, . w; were derived using a 0 – 1 loss function. Prove ... that these decision functions minimize the probability of error. Find p(c) and show that p(c) is maximum, when p(x |w;) p(w;) is maximum. Assume that the probability of error p(e) is 1 – p(c) where p(c) is probability of being correct and for a pattern vector x belonging to class W¡, p(c|x) = p(w;|x).
Transcribed Image Text:The Ваyes decision functions d;(x) = p(x|w;) p(w;), j = 1, 2, . w; were derived using a 0 – 1 loss function. Prove ... that these decision functions minimize the probability of error. Find p(c) and show that p(c) is maximum, when p(x |w;) p(w;) is maximum. Assume that the probability of error p(e) is 1 – p(c) where p(c) is probability of being correct and for a pattern vector x belonging to class W¡, p(c|x) = p(w;|x).
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