The amazing Gauss.
The familiar Gaussian distribution turns out to be the unique solution for a another important problem.
Suppose, you only know the first moment (mean) and the second moment (noise power)? What is “the best” probability distribution, given this little information?
Out of the infinite number of possible distributions, the Gaussian distribution is ensured to be the best! This amazing result follows from the application of Claude Shannon’s information entropy.
In fact, the Gaussian distribution is not just the best, it is the only distribution which is consistent with the information given above. Amazing!