In this problem, we study a simple noisy communication channel. suppose that x is a binary signal that takes value −1 and 1 with equal probability. this signal x is sent through a noisy communication channel, and the medium of transmission adds an independent noise term. more precisely, the received signal is y=x+n, where n is standard normal, indpendendent of x. the decoder receives the value y of y, and decides whether x was 1 or −1, using the following decoding rule: it decides in favor of 1 if and only ifp(x=1|y=y)> 2p(x=−1|y=y) it turns out that the decoding rule can be expressed in the form: decide in favor of 1 if and only if y> t, for some threshold t. find the threshhold t. as an intermediate step, find p1≜p(x=1|y=y).p1=now find t. t=