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I really think the most "understandable" derivation of the arithmetic mean is that as a maximum-likelihood estimator of the mean of gaussian IID random variable
by azalemeth 6y ago
I really think the most "understandable" derivation of the arithmetic mean is that as a maximum-likelihood estimator of the mean of gaussian IID random variables. It literally requires a touch of calculus, and it pops out beautifully. Of course, proving it in general is a bit more involved, but...
- srean 6y agoOne can do without calculus in this case. Using the fact that a squared expression is positive one can show that the arithmetic mean is indeed the maximum likelihood estimator. For the general case one cant avoid calculus.