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Consider the estimator of the variance given by the formula: $(S')^2 = \frac{1}{n} \sum_{i=1}^{n}(Y_i − µ)^2$

Is this a biased or unbiased estimator?

I'm not sure if it is possible to prove this without any additional information. Is there something missing?

schrader21
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  • No, nothing is missing. What is the expected value of $(Y_1-\mu)^2$? – jbowman Jan 13 '20 at 23:50
  • Oh, the variance, right? – schrader21 Jan 13 '20 at 23:53
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    Well you do have to assume the mean $\mu$ is known to determine the unbiasedness of the variance estimate. Presumably also though not stated in the question is that the $Y_i$ are independent & identically distributed. This is an elementary question. so you should use the self study tag. – Michael R. Chernick Jan 14 '20 at 00:01
  • And what is the expected value of the average of a bunch of i.i.d. random variables, all with the same expected value? – jbowman Jan 14 '20 at 00:12

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