final_practice_2009

# B describe the neyman pearson test for the two cases

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: , µ1 , σ0 , σ1 and the quantities N 2 k=1 Yk and N k=1 Yk . (b) Describe the Neyman-Pearson test for the two cases 2 2 • µ0 = µ1 , σ0 &lt; σ1 2 2 • µ0 &lt; µ1 , σ0 = σ1 2 2 (c) Find the threshold and the Receiver Operating Characteristics for the case µ0 = µ1 , σ1 &gt; 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 hypothesis|H ) = 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...
View Full Document

## 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.

Ask a homework question - tutors are online