1 is x = Z+ where the noise is a sample from a Gaussian distribution of zero mean and identity covariance, 1 P. (E): 1 2 T exp V27 (1) (2) The goal of the system is to determine which codeword (Ho or 1) was transmitted given the observation of the signal x. a) Formulate the problem as one of decision theory. Clearly, the observation variable is the received signal X. Answer the following questions. what is the random variable Y that encodes the class of signal? what values can Y have, and under which conditions does it have each of those values