3} Bayesian Binary Detection Decision Rule {21) pts.) Consider a case where a transmitter can send 2 symbols {an and c1 respectively}, and a receiver can receive the signals being sent, but with AWGN (Additive White Gaussian Noise}. One needs to decide from X (the received signal) whether symbol 050 or {1.1 was sent. To be more specic, there are two hypotheses: H0: X=ag+W H1: X=a1+W Where H0 is the hypothesis that at] was sent, H1 is the hypothesis that .11 was sent, and W is the AWGN. Using a Bayesian appneach, one needs to nd the decision region X0 {and automatically X1 since the decision is binary), so that the probability of the total error is minimized. c) (10 pts.) Assume W ~ N(0, ow2), find the optimal decision rule to choose Ho over H1, as a function of Ow, P[Hol, P[Hi], ao, and a1