Consider example 3, and let Z = AW where W ~ N (0, I) is normalized IID Gaussian. The observation rv Y is a + Z given H = 0 and is b + Z given H = 1. Suppose the observed sample value y is transformed...

Consider example 3, and let Z = AW where W ~ N (0, I) is normalized IID Gaussian. The observation rv Y is a + Z given H = 0 and is b + Z given H = 1. Suppose the observed sample value y is transformed into v = A₁y. Explain why v is a sucient statistic for this detection problem (and thus why MAP detection based on v must yield the same decision as that based on y).