Page 73 - Introduction to Statistical Pattern Recognition
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3 Hypothesis Testing 55
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x2 x2
Fig. 3-2 Decision boundaries for normal distributions:
(a) XI f &; (b) XI = &.
(3.12)
Figure 3-2 shows two-dimensional examples for XI zC2 and C =&.
I
Example 2: Let us study a special case of (3.1 1) where
1 p; ... py-'
Pi 1
Mi =O and Xi = (3.13)
' Pi
py-' . . . Pi 1
This type of covariance matrix is often seen, for example, when stationary run-
dom processes are time-sampled to form random vectors. The explicit expres-
sions for Z;' and I Zi I are known for this covariance matrix as
