Page 104 - Introduction to Statistical Pattern Recognition
P. 104
86 Introduction to Statistical Pattern Recognition
0’ =E [{ h (X) - IO;]
= E[( (M2 - MI)Y(X - M;)]2 I Oil
= (M2 - M1)YE{(X - M,)(X - M;)T IO; }X4(M2 - MI)
= (M* - M1)Y(M* - MI) = 2q . (3.99)
The above holds because E { (X - Mj)(X - Mi)‘ IO, ] is Z, (=Z), as was shown
in (2.13).
Figure 3-15 shows the density functions of h(X) for o1 and y, and the
Fig. 3-15 Density functions of h(X) for normal distributions with equal co-
variances.
hatched parts correspond to the error probabilities which are due to the Bayes
test for minimum error. Therefore,
(3.100)
(3.101)
where a(.) is the normal error function of (3.39), and
