Question: Binary hypothesis test and SNR Consider the binary choice in Gaussian noise, as shown in Example 5.2. With the threshold of k/2, the SNR is

Binary hypothesis test and SNR Consider the binary choice in Gaussian noise, as shown in Example 5.2. With the threshold of k/2, the SNR is also maximized at the decision point. Since the possible signal values are known, maximization of the SNR means that the hypothesized noise variance is minimized when the decision boundaries are optimally chosen. Prove that the SNR is maximized when the threshold is k/2.

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