1. The problem statement, all variables and given/known data The signal s(t) is a deterministic signal with the finite duration (0,Ts) and the energy Es=∫s2(t)dt. In the following system, n(t) is a normal noise with the mean zero and the power spectral density Gn(f)=η/2. Show that no(Ts) has a normal distribution with the mean zero and the variance (η/2)Es. 2. Relevant equations E[no(t)]=H(0)E[n(t)] Rnono(τ)=h(τ)*h(-τ)*Rnn(τ) (* is the convolution) var(no(t))=Rnono(0)=∫Gno(f)df (since E[no(t)]=0) Gno(f)=|H(f)|2Gn(f) 3. The attempt at a solution I know how to derive mean and variance , but don't know how to show normality. The prof just mentioned in the class that if the input to a LTI system is normal, then the output is so. How to prove this? Thanks in advance.