Consider a baseband binary PAM receiver shown below. The additive channel noise n(t) is whit with power spectral density S_{k(}f)=N_{0}/2=10^{-20} W/Hz. The low-pass is ideal with unity gain and cutoff frequency 1MHZ Let Y_{k} represent the random variable y(t_{k})

Y_{k}=N_{k} if transmitted bit b_{k}=0

Y_{k}=a+N_{k } if transmitted bit b_{k}=1

Where Nk represents the noise sample value. The noise sample has a probability density function P_{Nk}(n)=0.5?e^{-?|n| }(This has mean zero and variance 2/?^{2}) Assume transmitted bits to be equiprobable and thresold Z is set to a/2=10^{-6}v

The probability of bit error is