(10 points) Oscar uses his high-speed modem to connect to the internet. The modem transmits zeros and ones by sending signals -1 and +1, respectively. We assume that any given bit has probability p of being a zero. The network cable introduces additive zero-mean Gaussian noise with variance o² (so, the receiver at the other end receives a signal which is the sum of the transmitted signal and the channel noise). The value of the noise is assumed to be independent of the encoded signal value. Let a be a constant between -1 and 1. The receiver at the other end decides that the signal - 1 (respectively, +1) was transmitted if the value it receives is less (respectively, more) than a. (a) (3 pts) What is P[error when a +1 is transmitted]? (b) (3 pts) What is P[error when a -1 is transmitted]? (c) (2 pts) Considering both cases in (a) and (b), what is the overall probability of making an error? (d) (2 pts) Find a numerical answer for overall error probability assuming that p = 2/5, a = ½, and o²=1/4.