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This exercise looks at the "signal detection" problem in lecture (Fri 2/3) from the per- spective of odds. Recall the set-up: a signal X is sent with probability for some 0< X = -1 with probability p +1 with probability 1-p A noise Z~ N(0.1) is added to the signal during the process of

This exercise looks at the "signal detection" problem in lecture (Fri 2/3) from the per- spective of odds. Recall the set-up: a signal X is sent with probability for some 0< X = -1 with probability p +1 with probability 1-p A noise Z~ N(0.1) is added to the signal during the process of

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Exercise 3 This exercise looks at the "signal detection" problem in lecture (Fri 2/3) from the per- spective of odds. Recall the set-up: a signal X is sent with probability X = +1 with probability p with probability 1-p for some 0 < p < 1. A noise Z~ N(0,1) is added to the signal during the process of transmission, so that the signal received is Y = X + Z. (i) Compute the prior odds of X = +1 to X = -1. (ii) Suppose we receive Y = y. Compute the likelihood ratio (a.k.a. Bayes factor) fy(y X = +1) fy (y X = -1) as a function of y. When is this greater than, equal to, and less than 1, respectively? (iii) Compute the posterior odds of X = +1 to X -1 as a function of y. When is this greater than, equal to, and less than the prior odds, respectively? =
Transcribed Image Text:Exercise 3 This exercise looks at the "signal detection" problem in lecture (Fri 2/3) from the per- spective of odds. Recall the set-up: a signal X is sent with probability X = +1 with probability p with probability 1-p for some 0 < p < 1. A noise Z~ N(0,1) is added to the signal during the process of transmission, so that the signal received is Y = X + Z. (i) Compute the prior odds of X = +1 to X = -1. (ii) Suppose we receive Y = y. Compute the likelihood ratio (a.k.a. Bayes factor) fy(y X = +1) fy (y X = -1) as a function of y. When is this greater than, equal to, and less than 1, respectively? (iii) Compute the posterior odds of X = +1 to X -1 as a function of y. When is this greater than, equal to, and less than the prior odds, respectively? =
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