4400_645_Fall04_Lecture6

We want to determine the decision rule and the

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Unformatted text preview: random variable with zero-mean and unit variance. We want to determine the decision rule and the decision space. Example 2 (Bayes Approach) For the binary channel shown below, find the likelihood ratio test and the test statistics. 1− λ 0 λ1 λ0 1 − λ0 © Dr. O. C. Ugweje, University of Akron Page 4 Examples (cont’d) Electrical & Computer Engineering Example 3 (Bayes Approach) Consider the hypothesis testing problem H1 : Y ~ P0 = N ( µ0 , σ 2 ) H 0 : Y ~ P = N ( µ1 , σ 2 ) 1 Determine the decision rule and the decision space. Example 4 (Bayes & Minimax Approach) Suppose Y is a random variable the following hyposeses 2 ( y + 1) , 0 ≤ y ≤ 1 H 0 : Y ~ P0 ( y ) = 3 0, else 1, 0 ≤ y ≤ 1 H1 : Y ~ P ( y ) = 1 0, else © Dr. O. C. Ugweje, University of Akron Page 5 Example 4 (cont’d) Electrical & Computer Engineering A. Find the Bayes Rule and the minimum Bayes risk for testing H0 vs. H1 with uniform cost and equal priors. B. Find the Minimax Rule and Minimax Risk for uniform cost. Solution: C00 = C11 = 0 For uniform cost Cij = 1-dij ⇒ C01 = C10 = 1 C - C00 π 0 P(H0)=P(H1) ⇒ 10 ⋅ = 1=γ C01 - C11 π 1 For (A) 3 , 0 ≤ y ≤1 P ( y | H1 ) P ( y ) L( y ) = 1 =1 = 2 ( y +...
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This note was uploaded on 10/01/2010 for the course ELEC 6111 taught by Professor Brown during the Spring '10 term at E. Illinois.

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