Let Y be the observation rv for a binary detection problem, let y be the observed sample value. Let v = f(y) be a sucient statistic and let V be the corresponding random variable. Show that the...

Let Y be the observation rv for a binary detection problem, let y be the observed sample value. Let v = f(y) be a sucient statistic and let V be the corresponding random variable. Show that the likelihood ratio,
(y), is equal to p_V/H(f(y)|1)/p_V|H
(f(y)|0). In other words, show that the likelihood ratio of a sucient statistic is the same as the likelihood ratio of the original observation.