I have read that "Gauss proved that the best estimate for a random variable is the average." Can someone provide Gauss' publication containing that proof? To be clear, I am not looking for you to perform a derivation, instead, I am simply looking for a citation. Thanks.
This is a compendium of Gauss's contributions to statistics. If Gauss did indeed accomplish what you assert ... you should be able to find it here.... If not then the assertion may not be true.
I skimmed this rather exhaustive paper and could not precisely find what you are looking for .... but perhaps another scan will pick it up.