# How to calculate mean and Variance of Gaussian-distributed random noise?

I have been given a Gaussian-distributed random noise n(t) which has an average power of 5 mW. How can I calculate the mean and variance of noise n(t)? Any suggestions? Thanks!

• Please tell us in what form you were "given" the Gaussian-distributed random noise. Don't be shy; tell us exactly what you were "given". Have you been told the power spectral density? Were you told that is white Gaussian noise? band-limited white Gaussian noise? Is it continuous-time noise or discrete-time noise? Apr 17, 2021 at 14:02
• @DilipSarwate Hi! In The question I have only been given that A Gaussian-distributed random noise n(t) has an average power of 5 mW. Apr 17, 2021 at 14:13

If the values for each sample of $$n(t)$$ are given, then the mean and variance can be estimated using the equations for sample mean and sample variance, which is trivial so I assume the OP is only given that it is Gaussian-distributed with average power of 5 mW. From that alone, there is no way to know what the mean of the signal is since it hasn't been specified that the process is "zero-mean" or not. If the signal does have a mean value, it will contribute to the total power so this must be specified.
• How can the mean and variance be computed from sample values? Did you mean estimated as in sample mean and sample variance the way the folks over at stats.SE do it when given $N$ (independent) sample values of an alleged Gaussian random variable? Apr 17, 2021 at 14:05