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Unformatted text preview: the likelihood matrix for the observation (X, Y ) and indicate the ML decision rule. To be
deﬁnite, break ties in favor of H1 .
(b) Find pfalse alarm and pmiss for the ML rule found in part (a).
(c) Suppose, based on past experience, prior probabilities π1 = P (H1 ) = 0.2 and π0 = P (H0 ) = 0.8
are assigned. Compute the joint probability matrix and indicate the MAP decision rule. 60 CHAPTER 2. DISCRETE-TYPE RANDOM VARIABLES (d) For the MAP decision rule, compute pfalse alarm , pmiss , and the unconditional probability of error
pe = π0 pfalse alarm + π1 pmiss .
(e) Using the same priors as in part (c), compute the unconditional error probability, pe , for the
ML rule from part (a). Is it smaller or larger than pe found for the MAP rule in (d)?
Solution: (a) The likelihood matrix for observation (X, Y ) is the following.
(X, Y ) → (0, 0) (0, 1) (0, 2) (1, 0) (1, 1) (1, 2) (2, 0) (2, 1) (2, 2)
0.01 0.01 0.08 0.03 0.03 0.24 0.06 0.06 0.48
0.56 0.16 0.08 0.07 0.02 0.01 0.07 0.02 0.01. The ML deci...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.
- Spring '08
- The Land