In this problem, we consider target detection in a radar system. Upon observing a realization a of therandom variable X which represents the return signal in noise, a decision has to be made as towhether the target is present or absent. The target amplitude is known and equal to A > 0. Theobservation is made in zero-mean Gaussian noise W whose variance is known and equal to 2. Ifthe target is present (hypothesis H1), X = A+W. If the target is absent (hypothesis Ho), X = W. The likelihood ratio test for this problem is stated as follows: If fi (x)/fo(x) > n= decide infavor of H1; otherwise, decide in favor of Ho.lf n = 1, determine the probability of correctdetection (target declared present when indeed present) and the probability of false alarm (targetdeclared present when in fact absent). Express these probabilities in terms of the ratio a = A/o. Ifa = 4, which of the following represents the correct probabilities of false alarm and correctdetection, respectively?O None of the answers are correct.2% and 98%5% and 98%O 5% and 95%

None of the answers are correct.

ro-mean Gaussian noise W whose variance is known othesis H1), X = A + W. If the target is absent (hy for this problem is stated as follows: If fi (x)/fo(x) ecide in favor of Ho.lf n = 1, determine the probabi present when indeed present) and the probability o fact absent). Express these probabilities in terms of t wing represents the correct probabilities of false alar

ro-mean Gaussian noise W whose variance is known othesis H1), X = A + W. If the target is absent (hy for this problem is stated as follows: If fi (x)/fo(x) ecide in favor of Ho.lf n = 1, determine the probabi present when indeed present) and the probability o fact absent). Express these probabilities in terms of t wing represents the correct probabilities of false alar

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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