This preview shows page 1. Sign up to view the full content.
Unformatted text preview: sions are indicated by the underlined elements. The larger number in each column is
underlined, with the tie in case (0, 2) broken in favor of H1 , as speciﬁed in the problem statement.
Note that the row sums are both one.
(b) For the ML rule, pfalse alarm is the sum of the entries in the row for H0 in the likelihood matrix
that are not underlined. So pfalse alarm = 0.08 + 0.02 + 0.01 + 0.02 + 0.01 = 0.14.
For the ML rule, pmiss is the sum of the entries in the row for H1 in the likelihood matrix that are
not underlined. So pmiss = 0.01 + 0.01 + 0.03 + 0.06 = 0.11.
(c) The joint probability matrix is given by
(X, Y ) → (0, 0) (0, 1) (0, 2) (1, 0) (1, 1) (1, 2) (2, 0) (2, 1) (2, 2)
H1
0.002 0.002 0.016 0.006 0.006 0.048 0.012 0.012 0.096
H0
0.448 0.128 0.064 0.056 0.016 0.008 0.056 0.016 0.008.
(The matrix speciﬁes P (X = i, Y = j, Hk ) for each hypothesis Hk and for each possible observation
value (i, j ). The 18 numbers in the matrix sum to one. The MAP decisions are indicated by
the underlined elements in the joint probability m...
View
Full
Document
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
 Zahrn
 The Land

Click to edit the document details