FRM Part I · FRM Exam Part I · Sample Moments
Which statement about the sample mean as an estimator of the population mean for i.i.d. data with finite variance is correct?
The sample mean is unbiased, and its variance equals the population variance divided by n. Unbiasedness holds for any distribution with a finite mean, not just the normal, and it is not biased in small samples. The n-1 divisor applies to the sample variance estimator.
- AIt is biased in small samples but consistent as n grows
- BIt is unbiased, and its variance equals the population variance divided by nCorrect
- CIt is unbiased only if the underlying data are normally distributed
- DIt is unbiased, and its variance equals the population variance divided by n-1
Explanation
For i.i.d. data, E[sample mean] = mu regardless of distribution, and Var = sigma^2/n. Normality is not needed for unbiasedness, and n-1 is not the divisor for the variance of the mean.
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