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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!

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  • $\begingroup$ 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? $\endgroup$
    – Dilip Sarwate
    Apr 17, 2021 at 14:02
  • $\begingroup$ @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. $\endgroup$
    – Pressing_Keys_24_7
    Apr 17, 2021 at 14:13

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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.

The variance is the portion of the power that is not included in the mean. Since units of power were provided, then the resistance would need to also be given in order to provide units for any non-zero mean (voltage or current) if there is a mean value.

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    $\begingroup$ 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? $\endgroup$
    – Dilip Sarwate
    Apr 17, 2021 at 14:05
  • $\begingroup$ Thanks for the answer! Consider the mean to be zero, so now how can I calculate the variance? Thanks! $\endgroup$
    – Pressing_Keys_24_7
    Apr 17, 2021 at 15:29
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    $\begingroup$ @Pressing_Keys_24_7 See my second paragraph and let me know what is still confusing you about that sentence. You have zero mean, so mean is zero. Therefore all the power is the variance. $\endgroup$
    – Dan Boschen
    Apr 17, 2021 at 15:32
  • $\begingroup$ Got it! Thanks a lot for the help! $\endgroup$
    – Pressing_Keys_24_7
    Apr 17, 2021 at 15:34

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