Please explain as detailed as possible. In other words, what informaton lead to

Question

Please explain as detailed as possible. In other words, what informaton lead to answer.

True/False. You must explain each answer (a) When x ~ N(0, sigma^2_0) under H_0 and x ~ N(0, sigma^2_1) under H_1, the decision region depends only on the ratio sigma^2_0 sigma^2_1. (b) In choosing between hypotheses H_0 and H_1, minimizing the Bayes risk requires knowledge of the probability of H_0. (c) When detecting a signal in Gaussian noise, the test statistic is linear in the received data. (d) The ROC curve for any detection statistic is monotonic.

Explanation / Answer

A) ANSWER-

FALSE

THE RATIO IS 0/SIGMA 1 SQUARE

B) ANSWER-

FALSE

BOTH PROBABILITY ARE SAME

c) answer-

TRUE

Detection of a sinusoidal signal in additive white Gaussian noise with Rayleigh fading channel model. In typical detection scenario, the signal of interest can reach the detector/receiver following many different paths.

4) answer -

TRUE

Receiver Operating Characteristic (ROC)

This review provides the basic principle and rational for ROC analysis of rating and continuous diagnostic test results versus a gold standard. Derived indexes of accuracy, in particular area under the curve (AUC) has a meaningful interpretation for disease classification from healthy subjects. The methods of estimate of AUC and its testing in single diagnostic test and also comparative studies, the advantage of ROC curve to determine the optimal cut off values and the issues of bias and confounding have been discussed.

Key Words: Sensitivity, Specificity, ROC curve, Area under the curve (AUC), Parametric, Nonparametric, Bias

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