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Unformatted text preview: , µ1 , σ0 , σ1 and the quantities N
2
k=1 Yk and N
k=1 Yk . (b) Describe the NeymanPearson test for the two cases
2
2
• µ0 = µ1 , σ0 < σ1
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2
• µ0 < µ1 , σ0 = σ1
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2
(c) Find the threshold and the Receiver Operating Characteristics for the case µ0 = µ1 , σ1 > σ0 with N = 1. 2 2. Consider hypothesis testing problem based on the observation of y .
(a) Assume that the two hypotheses H0 and H1 are equally likely, P0 = P1 = 1/2. The conditional distribution is
given by
1, 0 ≤ y ≤ 1
p(y H0 ) =
0 else
Problem 3 (40 points)
2y, 0 ≤ y ≤ 1
Consider a hypothesisH ) =
p(y testing problem based on the observation of y .
1
0 else
(a) Assume that the two hypotheses, H0 and H1 are equally likely, i.e., P0 = P1 = 2.
which may be shown graphically1/as The conditional distribution is given in the following graph.
Py H (y H = 0) Py H (y H = 1) 2 1 PSfrag replacements
1 1 That is Specify the MAP decision rule and compute the resulting 1, 0 ≤ y ≤ 1 of error.
probability py H (y H0) = , (b) Specify the decision rule which minimizes the probability of mi...
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This note was uploaded on 01/08/2013 for the course ECE 531 taught by Professor Natasha during the Spring '10 term at Ill. Chicago.
 Spring '10
 Natasha

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