# Mean of experiment results is the maximum likelihood estimator only when the distribution of error is gaussian.

We want to find parameter $\mu$. So we have done some experiments. Let the error of measurements be i.i.d. Prove the mean of the results is the maximum likelihood for $\mu$ only when the distribution of errors is gaussian(let the distribution of error be differentiable as much as necessary).

• A classic problem, so I wonder where exactly do you encounter trouble? Did you try anything at all? – Nap D. Lover Jan 29 '18 at 19:27
• I am a math student with no background in statistics, so it wasn’t an easy question for me. I wrote the equation for maximum likelihood function but I couldn’t get the result that the error should have gaussian distribution. Proof of reverse is easy. When I write the pdf of gaussian in the ML equation, it turns out the mean. – fof Jan 30 '18 at 9:20