Suppose a wireless communication system consists of a transmitter and a receiver.If the transmitter emits a radio signal with transmission amplitude x, this signal is attenuated by the air and is received by the receiver together with noise,denoted byN. Let Y = hx+N be the received signal amplitude, where h = 0.1 is the attenuation factor and N is a Gaussian random variable with mean µ = 0 and variance σ2 = 4.

(a) Find the pdf fY (y) of the received signal amplitude Y for x = 1.

(b) Suppose the receiver output is zero if Y 0 and one if Y ≥ 0. An error is said to occur if the receiver output is not equal to the transmitted one. Find the probability of error, given the transmitted amplitude is one.