Question: A transmitter sends out a signal X~N(1,1/4). If x is the original signal, then because of some noise the receiver gets a signal Y which is normal with mean a+bx and standard deviation b|x| for some constants a and b such that b > 0. If it is known that E(Y) = 0, var(Y) = 3, then (a) find a and b, (b) cov(X, Y) and (c) correlation coefficient ρ(X, Y).