The received signal R in a digital communication system corresponds to one of two hypotheses: Ho : R - Gaussian(0,2 H:R-Gaussian(1,22) (a) The maximum-likelihood decision rule can be stated in the form "Decide that H1 is the true hypothesis if and only if R>n." What is the value of n, and what is the value of Ps, the false alarm probability of the maximum-likelihood decision rule? (b) Now suppose that the received signal R is passed through a quantizer whose output Sis 5 -a, if RC-1 O, if-1SRS +1 +Q, if R > +1 and the decision is made based on the value of S. Complete the likelihood matrix shown below, and indicate on it the maximum likelihood decision rule by shading entries. S=0 S = + HO HI (c) For the maximum-likelihood decision rule of part (b), what is Ps? The received signal R in a digital communication system corresponds to one of two hypotheses: Ho : R - Gaussian(0,2 H:R-Gaussian(1,22) (a) The maximum-likelihood decision rule can be stated in the form "Decide that H1 is the true hypothesis if and only if R>n." What is the value of n, and what is the value of Ps, the false alarm probability of the maximum-likelihood decision rule? (b) Now suppose that the received signal R is passed through a quantizer whose output Sis 5 -a, if RC-1 O, if-1SRS +1 +Q, if R > +1 and the decision is made based on the value of S. Complete the likelihood matrix shown below, and indicate on it the maximum likelihood decision rule by shading entries. S=0 S = + HO HI (c) For the maximum-likelihood decision rule of part (b), what is Ps