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# Chapter 5 Sample moments

#### DenisAmbrosov

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May someone explain how to interpret this part: see picture.

#### lushukai

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Hi @DenisAmbrosov ,

From left to right, the sum of the population mean over n iterations divided by n equals the population mean.

Not too sure what your question is, perhaps you can be more specific?

#### DenisAmbrosov

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Hi @DenisAmbrosov ,

From left to right, the sum of the population mean over n iterations divided by n equals the population mean.

Not too sure what your question is, perhaps you can be more specific?
I just can't understand. E[mu-hat]. Why mu-hat? As I understand mu-hat is for sample mean.But here I have E[mu-hat(sample mean)] = population mean

#### lushukai

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Dear @DenisAmbrosov ,

I think the math is trying to say - the expectation of the sample mean or the average of many sample means should give you the population mean, thanks.

#### DenisAmbrosov

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Dear @DenisAmbrosov ,

I think the math is trying to say - the expectation of the sample mean or the average of many sample means should give you the population mean, thanks.
I got it. Thank you!

#### DenisAmbrosov

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What does asymptotically unbiased mean?

#### lushukai

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Hi @DenisAmbrosov ,

The term asymptotically unbiased just explains the math in words. The word asymptotically comes from the word asymptote, which is a line that the curve seems to approach as it approaches infinity, but never really touches. The same with the estimator, as the sample size goes to infinity, the estimator becomes unbiased - never overestimating or underestimating the population statistic.