Noise pdf Gaussian

Question

Why the probability distribution function of the noise in a channel is Gaussian (normal distribution)? Intuitive discussion is appreciated.

Answer 1

You may think of noise as the result of many, many independant small random influences adding up. Then the central limit theorem says that this can be approximated by the normal distribution.

Answer 2

Another important property of Gaussian noise, is that if you pass it through a linear filter, the output will be Gaussian. So, many small independent sources of the noise, passing through linear filters, will result in Gaussian noise.