Page 140 - Introduction to Statistical Pattern Recognition

122 Introduction to Statistical Pattern Recognition

where 0 5 a < 1 and P2 = P3 =p.
(a) Find the Bayes boundary and plot it in the X-coordinate system.
(b) Write an expression for the probabilities of errors. (Do not evalu-
ate the integrals.)
MI = i], M2= 11,
11. Two distributions are normal with

E,=,,=[ 1 0.5 1.
PI =P2=0.5,

0.5 1

(a) Calculate the threshold values for the Wald sequential test for
=
=E~ and lo-’.
(b) Find the average number of observations required.
(c) Fixing the number of observations as obtained in (b), compute the
error of the sequential classifier with fixed m.

References

1. C. K. Chow, An optimum character recognition system using decision func-
tions, Trans. IRE Electronic Computers, EC-6, pp. 247-254,1957.
2. A. Wald, “Statistical Decision Functions,” Wiley, New York, 1950.
3. D. Blackwell and M. A. Girshick, “Theory of Games and Statistical Deci-
sions,” Wiley, New York, 1954.
4. T. S. Furguson, “Mathematical Statistics: A Decision Theoretic
Approach,” Academic Press, New York, 1967.
5. H. L. Van Trees, “Detection, Estimation, and Modulation Theory: Part I,”
Wiley, New York, 1968.
6. B. J. Burdick, Private communication, 1984.