(De Groot XXXXXXXXXXSuppose that, with probability to, a signal is present in a certain system at any given time, and that, with probability 10, no signal is present. A measurement made on the system...

(De Groot (1970)) Suppose that, with probability to, a signal is present in a certain system at any given time, and that, with probability 10, no signal is present. A measurement made on the system when a signal is present is normally distributed with mean 50 and variance 1, and a measurement made on the system when no signal is present is normally distributed with mean 52 and variance 1. Suppose that a measurement made on the system at a certain time has the value x. Show that the posterior probability that a signal is present is greater than the posterior probability that no signal is present, if