This is a Multipart Question.

NOTE:- Multiple Options Can be Correct, Please also give an explanation

In this problem, we consider target detection in a radar system. Upon observing a realization x of the random variable X which represents the return signal in noise, a decision has to be made as to whether the target is present or absent. The target amplitude is known and equal to A > U. The observation is made in zeromean Gaussian noise W ireaivatued], whose variance is known and equal to 0'2. If the target is present [hypothesis H. l, X = A + W. if the target is absent (hypothesis H0}, X = W. The likelihood ratio test for this problem is stated as follows: If fl(x)f1(x) > 11 => decide in favor of H]; otherwiSe. decide in favor of H0. if n = I, determine the probability of correct detection (target declared present when indeed present) and the probability of false alarm {target declared present when in fact absent). Express these probabilities in terms of the ratio (I = AM. If a = 4, which of the following represents the correct probabilities of false alarm and correct detection. respectively? Answers are rounded to the closest whole percentage value. 0 2% and 98% 0 None of the answers are correct. O 5% and 95% O 5% and 93% In the previous problem, if Instead of q = l the threshold is set so as to ensure probabilityr of false alarm of 1%, what will the probability of correct detection be? Mark the answer closest to the true value. 0 89% O 95% Q 99%