Isye 2027

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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) H1 0.01 0.01 0.08 0.03 0.03 0.24 0.06 0.06 0.48 H0 0.56 0.16 0.08 0.07 0.02 0.01 0.07 0.02 0.01. The ML deci...
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.

Ask a homework question - tutors are online