TEST BANK FOR Pattern Classification 2nd Edition B

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, ...