Problem 9. 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 telephone line introduces additive zero-mean Gaussian (normal) noise with variance o (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. (a) 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. Find a formula for the probability of making an error. (b) Find a numerical answer for the question of part (a) assuming that p = 2/5, a = 1/2 and o' = 1/4