TEST BANK FOR Pattern Classification 2nd Edition B
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Exam (elaborations)
Exam (elaborations) TEST BANK FOR Pattern Classification 2nd Edition B
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---443February 20222021/2022A+
- Exam (elaborations) TEST BANK FOR Pattern Classification 2nd Edition B 
We assume, without loss of generality, that for a given particular x we have 
P(ω2|x) ≥ P(ω1|x), and thus P(error|x) = P(ω1|x). We have, moreover, the 
normalization condition P(ω1|x)=1−P(ω2|x). Together these imply P(ω2|x) > 
1/2 or 2P(ω2|x) > 1 and 
2P(ω2|x)P(ω1|x) > P(ω1|x) = P(error|x). 
This is true at every x, and hence the integrals obey 
 
2P(ω2|x)P(ω1|x)dx ≥ 
 
P(error|x)dx. 
In short, ...
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